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## Bernstein, Dennis S.

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 Author ID: bernstein.dennis-s Published as: Bernstein, Dennis S.; Bernstein, D. S. Homepage: https://aero.engin.umich.edu/people/dennis-bernstein/ External Links: MGP · ORCID · Wikidata · Google Scholar · dblp · GND · IdRef
 Documents Indexed: 201 Publications since 1979, including 5 Books
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#### Co-Authors

 16 single-authored 59 Haddad, Wassim Michael 10 Bhat, Sanjay P. 10 Hyland, David C. 7 Chandrasekar, Jaganath 7 Hoagg, Jesse B. 7 Palanthandalam-Madapusi, Harish J. 7 Sparks, Andrew G. 7 Wang, Y. William 6 Aljanaideh, Khaled F. 6 Tyan, Feng 5 Chellaboina, Vijaya-Sekhar 5 Collins, Emmanuel G. jun. 5 Erwin, Richard Scott 5 Watson, Layne Terry 4 Chellaboina, Vijaysekhar 4 Coppola, Vincent T. 4 Hall, Steven R. 4 Oh, Jin Hyoung 4 Ridley, Aaron J. 4 Santillo, Mario A. 3 Corrado, Joseph R. 3 Drinčić, Bojana 3 Halevi, Yoram 3 Huang, Hsing-Hsin 3 Jun, Byung-Eul 3 Kapila, Vikram 3 Kishimoto, Yasuo 3 Lacy, Seth L. 3 McClamroch, N. Harris 3 Roup, Alexander V. 3 Teixeira, Bruno Otávio Soares 3 Van Pelt, Tobin H. 3 Venugopal, Ravinder 3 Wan, Chih-Jian 2 Aguirre, Luis Antonio 2 Akhtar, Suhail 2 Bupp, Robert T. 2 Chaturvedi, Nalin A. 2 D’Amato, Anthony M. 2 De Moor, Bart L. R. 2 Ge, Yuzhen 2 Gilbert, Elmer G. 2 Greeley, Scott W. 2 Holzel, Matthew S. 2 Michel, Anthony N. 2 Sanjeevini, Sneha 2 Torres, Leonardo Antônio Borges 2 Wilson, David A. 2 Yan, Jin 2 Žigić, Dragan 1 Ansari, Ahmad 1 Baksalary, Oskar Maria 1 Barrero, O. 1 Bruce, Adam L. 1 Clark, Robert L. 1 Dai, Shicong 1 Davis, Lawrence David 1 Fassois, Spilios D. 1 Frazho, Arthur E. 1 Friedman, Jonathan H. 1 Goel, Ankit 1 Hindman, Richard E. 1 Hollot, Christopher V. 1 Hong, Jeongho 1 How, Jonathan P. 1 Kabamba, Pierre T. 1 Kamaldar, Mohammadreza 1 King, James A. 1 Kirtikar, Siddharth 1 Kouba, Omran 1 Lum, Kai-Yew 1 MacMartin, Douglas G. 1 Madiwale, Appasaheb N. 1 Mendoza, O. Barrero 1 Moll, Victor Hugo 1 Mustafa, Denis 1 Nersesov, Sergey G. 1 Osburn, Scot L. 1 Padthe, Ashwani K. 1 Prach, Anna 1 Rao, Venkatesh G. 1 Ren, Zhang 1 Rern, Shuoh 1 Rizos, Demosthenis D. 1 Rosen, I. Gary 1 Scott, Erwin R. 1 So, Wasin 1 Sobolic, Frantisek M. 1 Sumer, E. Dogan 1 Tan, Xiaobo 1 Tekinalp, Ozan 1 Trenkler, Götz 1 Tsiotras, Panagiotis 1 Zattoni, Elena
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#### Serials

 40 IEEE Transactions on Automatic Control 35 International Journal of Control 18 Systems & Control Letters 14 Automatica 12 International Journal of Robust and Nonlinear Control 9 IEEE Control Systems 7 Journal of Guidance, Control and Dynamics 7 International Journal of Adaptive Control and Signal Processing 5 SIAM Journal on Control and Optimization 5 Optimal Control Applications & Methods 5 MCSS. Mathematics of Control, Signals, and Systems 4 Journal of Sound and Vibration 4 SIAM Journal on Matrix Analysis and Applications 4 Journal of Mathematical Systems, Estimation, and Control 2 Applied Mathematics and Computation 2 Journal of Optimization Theory and Applications 2 Dynamics and Control 2 Linear Algebra and its Applications 2 Journal of Vibration and Control 1 American Mathematical Monthly 1 International Journal of Theoretical Physics 1 Journal of the Franklin Institute 1 Journal of Computational and Applied Mathematics 1 1 Circuits, Systems, and Signal Processing 1 Dynamics and Stability of Systems 1 IEEE Transactions on Signal Processing 1 Journal of Global Optimization 1 Aequationes Mathematicae 1 Journal of Dynamic Systems, Measurement and Control 1 Scientia. Series A: Mathematical Sciences. New Series 1 Statistical Analysis and Data Mining
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#### Fields

 183 Systems theory; control (93-XX) 21 Linear and multilinear algebra; matrix theory (15-XX) 20 Calculus of variations and optimal control; optimization (49-XX) 16 Mechanics of particles and systems (70-XX) 12 Ordinary differential equations (34-XX) 7 Functional analysis (46-XX) 6 Numerical analysis (65-XX) 5 Statistics (62-XX) 5 Mechanics of deformable solids (74-XX) 4 General and overarching topics; collections (00-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Operator theory (47-XX) 3 Computer science (68-XX) 3 Operations research, mathematical programming (90-XX) 2 Functions of a complex variable (30-XX) 2 Geophysics (86-XX) 2 Information and communication theory, circuits (94-XX) 1 Combinatorics (05-XX) 1 Special functions (33-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Biology and other natural sciences (92-XX)

#### Citations contained in zbMATH Open

161 Publications have been cited 2,761 times in 2,184 Documents Cited by Year
Finite-time stability of continuous autonomous systems. Zbl 0945.34039
Bhat, Sanjay P.; Bernstein, Dennis S.
2000
Matrix mathematics. Theory, facts, and formulas. 2nd expanded ed. Zbl 1183.15001
Bernstein, Dennis S.
2009
Geometric homogeneity with applications to finite-time stability. Zbl 1110.34033
Bhat, S. P.; Bernstein, D. S.
2005
Continuous finite-time stabilization of the translational and rotational double integrators. Zbl 0925.93821
Bhat, Sanjay P.; Bernstein, Dennis S.
1998
Matrix mathematics. Theory, facts, and formulas with application to linear systems theory. Zbl 1075.15001
Bernstein, Dennis S.
2005
LQG control with an $$H_{\infty}$$ performance bound: A Riccati equation approach. Zbl 0674.93069
1989
A chronological bibliography on saturating actuators. Zbl 0841.93002
Bernstein, Dennis S.; Michel, Anthony N.
1995
A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon. Zbl 0986.93063
Bhat, Sanjay P.; Bernstein, Dennis S.
2000
The optimal projection equations for fixed-order dynamic compensation. Zbl 0555.93069
Hyland, David C.; Bernstein, Dennis S.
1984
The optimal projection equations for model reduction and the relationships among the methods of Wilson, Skelton, and Moore. Zbl 0583.93004
Hyland, David C.; Bernstein, Dennis S.
1985
Steady-state Kalman filtering with an $$H_{\infty}$$ error bound. Zbl 0684.93081
1989
Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and Popov theorems and their application to robust stability. I: Continuous-time theory. Zbl 0794.93095
1993
Controller design with regional pole constraints. Zbl 0747.93025
1992
Modeling and analysis of mass-action kinetics: nonnegativity realizability, reducibility, and semistability. Zbl 1395.93098
Chellaboina, VijaySekhar; Bhat, Sanjay P.; Haddad, Wassim M.; Bernstein, Dennis S.
2009
Nontangency-based Lyapunov tests for convergence and stability in systems having a continuum of equilibria. Zbl 1078.34031
Bhat, Sanjay P.; Bernstein, Dennis S.
2003
Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and Popov theorems and their application to robust stability. Part II: Discrete-time theory. Zbl 0806.93045
1994
Robust stabilization with positive real uncertainty: Beyond the small gain theorem. Zbl 0759.93062
1991
Robust static and dynamic output-feedback stabilization: Deterministic and stochastic perspectives. Zbl 0632.93056
Bernstein, Dennis S.
1987
Parameter-dependent Lyapunov functions and the Popov criterion in robust analysis and synthesis. Zbl 0821.93063
1995
Robust stability and performance analysis for state-space systems via quadratic Lyapunov bounds. Zbl 0701.93077
1990
The optimal projection equations for reduced-order state estimation. Zbl 0555.93056
Bernstein, Dennis S.; Hyland, David C.
1985
Nonquadratic cost and nonlinear feedback control. Zbl 0795.93041
Bernstein, Dennis S.
1993
Dynamic output feedback compensation for linear systems with independent amplitude and rate saturations. Zbl 0878.93028
Tyan, Feng; Bernstein, Dennis S.
1997
Mixed-norm $$H_ 2/H_{\infty}$$ regulation and estimation: The discrete- time case. Zbl 0728.93033
Haddad, Wassim M.; Bernstein, Dennis S.; Mustafa, Denis
1991
Semilinear Duhem model for rate-independent and rate-dependent hysteresis. Zbl 1365.93033
Oh, JinHyoung; Bernstein, Dennis S.
2005
The optimal projection equations with Petersen-Hollot bounds: Robust stability and performance via fixed-order dynamic compensation for systems with structured real-valued parameter uncertainty. Zbl 0648.93013
1988
Compartmental modeling and second-moment analysis of state space systems. Zbl 0782.93004
Bernstein, Dennis S.; Hyland, David C.
1993
Some explicit formulas for the matrix exponential. Zbl 0784.93036
Bernstein, Dennis S.; So, Wasin
1993
Second-order necessary conditions in optimal control: Accessory-problem results without normality conditions. Zbl 0497.49018
Gilbert, E. G.; Bernstein, D. S.
1983
Robust stability and performance via fixed-order dynamic compensation with guaranteed cost bounds. Zbl 0694.93021
1990
Parameter-dependent Lyapunov functions and the discrete-time Popov criterion for robust analysis. Zbl 0825.93667
1994
Subspace identification with guaranteed stability using constrained optimization. Zbl 1364.93162
Lacy, Seth L.; Bernstein, Dennis S.
2003
Arc-length-based Lyapunov tests for convergence and stability with applications to systems having a continuum of equilibria. Zbl 1248.93125
Bhat, Sanjay P.; Bernstein, Dennis S.
2010
Generalized Riccati equations for the full- and reduced-order mixed-norm $$H_ 2/H_{\infty}$$ standard problem. Zbl 0699.93025
1990
Asymptotic smooth stabilization of the inverted 3-D pendulum. Zbl 1367.93492
Chaturvedi, Nalin A.; McClamroch, N. Harris; Bernstein, Dennis S.
2009
Robust controller synthesis using the maximum entropy design equations. Zbl 0635.93057
Bernstein, Dennis S.; Greeley, Scott W.
1986
Inequalities for the trace of matrix exponentials. Zbl 0658.15018
Bernstein, Dennis S.
1988
Special issue on saturating actuators. Zbl 0828.00026
Bernstein, D. S. (ed.); Michel, A. N. (ed.)
1995
Discrete-time adaptive command following and disturbance rejection with unknown exogenous dynamics. Zbl 1367.93308
Hoagg, Jesse B.; Santillo, Mario A.; Bernstein, Dennis S.
2008
Robust stability for sampled-data control systems. Zbl 0684.93052
Bernstein, Dennis S.; Hollot, C. V.
1989
Robust stability and performance analysis for linear dynamic systems. Zbl 0689.93020
1989
Optimal periodic control: the $$\pi$$ test revisited. Zbl 0447.49028
Bernstein, Dennis S.; Gilbert, Elmer G.
1980
Some open problems in matrix theory arising in linear systems and control. Zbl 0765.93026
Bernstein, Dennis S.
1992
Experimental implementation of integrator backstepping and passive nonlinear controllers on the RTAC testbed. Zbl 0925.93352
Bupp, Robert T.; Bernstein, Dennis S.; Coppola, Vincent T.
1998
Limit cycle analysis of the verge and foliot clock escapement using impulsive differential equations and Poincaré maps. Zbl 1052.93044
Roup, Alexander V.; Bernstein, Dennis S.; Nersesov, Sergey G.; Haddad, Wassim M.; Chellaboina, Vijaysekhar
2003
Anti-windup compensator synthesis for systems with saturation actuators. Zbl 0831.93033
Tyan, Feng; Bernstein, Dennis S.
1995
Nonlinear feedback control with global stabilization. Zbl 0841.93067
Wan, Chih-Jian; Bernstein, Dennis S.
1995
Second-order systems with singular mass matrix and an extension of Guyan reduction. Zbl 0857.34003
Bhat, Sanjay P.; Bernstein, Dennis S.
1996
Dissipative $$H_ 2/H_ \infty$$ controller synthesis. Zbl 0807.93022
Haddad, Wassim M.; Bernstein, Dennis S.; Wang, Y. William
1994
Extensions of mixed-$$\mu$$ bounds to monotonic and odd monotonic nonlinearities using absolute stability theory. Zbl 0825.93672
Haddad, Wassim M.; How, Jonathan P.; Hall, Steven R.; Bernstein, Dennis S.
1994
Global stabilization of the spinning top with mass imbalance. Zbl 0837.93048
Lum, Kai-Yew; Bernstein, Dennis S.; Coppola, Vincent T.
1995
Internal model control in the shift and delta domains. Zbl 1367.93231
Hoagg, Jesse B.; Santillo, Mario A.; Bernstein, Dennis S.
2008
Robust $$H_{\infty}$$ control design for systems with structured parameter uncertainty. Zbl 0685.93022
1989
Homotopy methods for solving the optimal projection equations for the $$H_ 2$$ reduced order model problem. Zbl 0766.93009
Žigić, Dragan; Watson, Layne T.; Collins, Emmanuel G. jun.; Bernstein, Dennis S.
1992
On stable full-order and reduced-order LQG controllers. Zbl 0766.49023
Halevi, Yoram; Bernstein, Dennis S.; Haddad, Wassim M.
1991
A Popov criterion for uncertain linear multivariable systems. Zbl 0838.93058
Bernstein, Dennis S.; Haddad, Wassim M.; Sparks, Andrew G.
1995
Identification of FIR Wiener systems with unknown, non-invertible, polynomial non-linearities. Zbl 1050.93074
Lacy, Seth L.; Bernstein, Dennis S.
2003
Direct adaptive command following and disturbance rejection for minimum phase systems with unknown relative degree. Zbl 1134.93042
Hoagg, Jesse B.; Bernstein, Dennis S.
2007
Nonlinear feedback models of hysteresis. Zbl 1395.93232
Oh, Jinhyoung; Drincic, Bojana; Bernstein, Dennis S.
2009
Sequential design of decentralized dynamic compensators using the optimal projection equations. Zbl 0642.93006
Bernstein, Dennis S.
1987
The majorant Lyapunov equation: A nonnegative matrix equation for robust stability and performance of large scale systems. Zbl 0643.93006
Hyland, David C.; Bernstein, Dennis S.
1987
Lyapunov-stable discrete-time model reference adaptive control. Zbl 1127.93337
Akhtar, S.; Bernstein, D. S.
2005
Optimal output feedback for nonzero set point regulation. Zbl 0624.93076
1987
Global stabilization of systems containing a double integrator using a saturated linear controller. Zbl 0980.93068
Tyan, Feng; Bernstein, Dennis S.
1999
Parameter consistency and quadratically constrained errors-in-variables least-squares identification. Zbl 1209.93165
Palanthandalam-Madapusi, Harish J.; van Pelt, Tobin H.; Bernstein, Dennis S.
2010
$$l$$-delay input and initial-state reconstruction for discrete-time linear systems. Zbl 1205.94038
Kirtikar, Siddharth; Palanthandalam-Madapusi, Harish; Zattoni, Elena; Bernstein, Dennis S.
2011
Gain-constrained Kalman filtering for linear and nonlinear systems. Zbl 1390.94437
Teixeira, Bruno Otávio Soares; Chandrasekar, Jaganath; Palanthandalam-Madapusi, Harish J.; Tôrres, Leonardo Antônio Borges; Aguirre, Luis Antonio; Bernstein, Dennis S.
2008
Spacecraft tracking using sampled-data Kalman filters: an illustrative application of extended and unscented estimators. Zbl 1395.93548
Teixeira, Bruno O. S.; Santillo, Mario A.; Erwin, R. Scott; Bernstein, Dennis S.
2008
Direct adaptive dynamic compensation for minimum phase systems with unknown relative degree. Zbl 1366.93576
Hoagg, Jesse B.; Bernstein, Dennis S.
2007
Optical projection equations for reduced-order modelling, estimation, and control of linear systems with multiplicative white noise. Zbl 0631.93077
Bernstein, D. S.; Hyland, D. C.
1988
Induced convolution operator norms of linear dynamical systems. Zbl 1031.93090
Chellaboina, Vijay-Sekhar; Haddad, Wassim M.; Bernstein, Dennis S.; Wilson, David A.
2000
Combined $$L_ 2/H_{\infty}$$ model reduction. Zbl 0675.93014
1989
Optimal nonlinear, but continuous, feedback control of systems with saturating actuators. Zbl 0843.93025
Bernstein, Dennis S.
1995
Robust stability and performance via fixed-order dynamic compensation: The discrete-time case. Zbl 0785.93073
Haddad, Wassim M.; Huang, Hsing-Hsin; Bernstein, Dennis S.
1993
Adaptive stabilization of a class of nonlinear systems with nonparametric uncertainty. Zbl 1015.93056
Roup, Alexander V.; Bernstein, Dennis S.
2001
Nonlinear system identification using Hammerstein and nonlinear feedback models with piecewise linear static maps. Zbl 1039.93015
Van Pelt, Tobin H.; Bernstein, Dennis S.
2001
Adaptive stabilization of nonlinear oscillators using direct adaptive control. Zbl 1017.93095
Hong, Jeongho; Bernstein, Dennis S.
2001
Probability-one homotopy algorithms for solving the coupled Lyapunov equations arising in reduced-order $$H^2/H^\infty$$ modeling, estimation, and control. Zbl 1028.93011
Wang, Y.; Bernstein, D. S.; Watson, L. T.
2001
On the equality between rank and trace of an idempotent matrix. Zbl 1206.15006
Baksalary, Oskar Maria; Bernstein, Dennis S.; Trenkler, Götz
2010
Robust, reduced-order, nonstrictly proper state estimation via the optimal projection equations with guaranteed cost bounds. Zbl 0642.93055
1988
Optimal reduced-order observer-estimators. Zbl 0753.93013
1990
Generalized mixed-$$\mu$$ bounds for real and complex multiple-block uncertainty with internal matrix structure. Zbl 0857.93074
Haddad, Wassim M.; Bernstein, Dennis S.; Chellaboina, Vijaya-Sekhar
1996
Subspace identification for nonlinear systems with measured-input nonlinearities. Zbl 1086.93011
Lacy, S. L.; Bernstein, D. S.
2005
The optimal projection equations for fixed-order sampled-data dynamic compensation with computation delay. Zbl 0593.93035
Bernstein, Dennis S.; Davis, Lawrence D.; Greeley, Scott W.
1986
Optimal projection equations for discrete-time fixed-order dynamic compensation of linear systems with multiplicative white noise. Zbl 0615.93077
1987
Robust controller synthesis via shifted parameter-dependent quadratic cost bounds. Zbl 0952.93045
Kapila, Vikram; Haddad, Wassim M.; Erwin, Richard S.; Bernstein, Dennis S.
1998
Lyapunov-based backward-horizon adaptive stabilization. Zbl 1033.93061
Venugopal, Ravinder; Rao, Venkatesh G.; Bernstein, Dennis S.
2003
Why are some hysteresis loops shaped like a butterfly? Zbl 1235.93062
Drinčić, Bojana; Tan, Xiaobo; Bernstein, Dennis S.
2011
Thermodynamic modelling of interconnected systems. I: Conservative coupling. Zbl 1237.70057
Kishimoto, Y.; Bernstein, D. S.
1995
Matrix pencils and existence conditions for quadratic programming with a sign-indefinite quadratic equality constraint. Zbl 1201.90148
Palanthandalam-Madapusi, Harish J.; Van Pelt, Tobin H.; Bernstein, Dennis S.
2009
State estimation for linear and nonlinear equality-constrained systems. Zbl 1165.93033
Teixeira, Bruno O. S.; Chandrasekar, Jaganath; Tôrres, Leonardo A. B.; Aguirre, Luis A.; Bernstein, Dennis S.
2009
Duhem modeling of friction-induced hysteresis: experimental determination of gearbox stiction. Zbl 1395.93104
Padthe, Ashwani K.; Drincic, Bojana; Oh, Jinhyoung; Rizos, Demosthenis D.; Fassois, Spilios D.; Bernstein, Dennis S.
2008
A subspace algorithm for simultaneous identification and input reconstruction. Zbl 1191.93103
Palanthandalam-Madapusi, Harish J.; Bernstein, Dennis S.
2009
Scalar, vector, and matrix mathematics. Theory, facts, and formulas. Revised and expanded edition. Zbl 1396.15001
Bernstein, Dennis S.
2018
Minimum modelling retrospective cost adaptive control of uncertain Hammerstein systems using auxiliary nonlinearities. Zbl 1317.93157
Yan, Jin; Bernstein, Dennis S.
2014
Closed-loop identification of unstable systems using noncausal FIR models. Zbl 1359.93116
Aljanaideh, Khaled F.; Bernstein, Dennis S.
2017
Energy flow modelling of interconnected structures: A deterministic foundation for statistical energy analysis. Zbl 1046.74521
Kishimoto, Yasuo; Bernstein, Dennis S.; Hall, Steven R.
1995
On the gap between $$H_ 2$$ and entropy performance measures in $$H_{\infty}$$ control design. Zbl 0692.93026
1990
Homotopy approaches to the $$H_ 2$$ reduced order model problem. Zbl 0770.93018
Žigić, Dragan; Watson, Layne T.; Collins, Emmanuel G. jun.; Bernstein, Dennis S.
1993
Global asymptotic stabilization of the spinning top. Zbl 0828.93056
Wan, Chih-Jian; Coppola, Vincent T.; Bernstein, Dennis S.
1995
Deadbeat unknown-input state estimation and input reconstruction for linear discrete-time systems. Zbl 1415.93246
Ansari, Ahmad; Bernstein, Dennis S.
2019
Scalar, vector, and matrix mathematics. Theory, facts, and formulas. Revised and expanded edition. Zbl 1396.15001
Bernstein, Dennis S.
2018
Closed-loop identification of unstable systems using noncausal FIR models. Zbl 1359.93116
Aljanaideh, Khaled F.; Bernstein, Dennis S.
2017
A behavioral equation framework for time-domain transmissibilities. Zbl 1357.93027
Aljanaideh, Khaled F.; Bernstein, Dennis S.
2017
Adaptive control of nonminimum-phase systems using shifted Laurent series. Zbl 1359.93222
Dai, Shicong; Ren, Zhang; Bernstein, Dennis S.
2017
Time-domain analysis of sensor-to-sensor transmissibility operators. Zbl 1371.93049
Aljanaideh, Khaled F.; Bernstein, Dennis S.
2015
On the role of subspace zeros in retrospective cost adaptive control of non-square plants. Zbl 1328.93146
Sumer, E. Dogan; Bernstein, Dennis S.
2015
Minimum modelling retrospective cost adaptive control of uncertain Hammerstein systems using auxiliary nonlinearities. Zbl 1317.93157
Yan, Jin; Bernstein, Dennis S.
2014
A matrix nullspace approach for solving equality-constrained multivariable polynomial least-squares problems. Zbl 1309.93046
Hölzel, Matthew S.; Bernstein, Dennis S.
2014
From polynomial matrices to Markov parameters and back: Theory and numerical algorithms. Zbl 1241.93017
Holzel, Matthew S.; Bernstein, Dennis S.
2012
$$l$$-delay input and initial-state reconstruction for discrete-time linear systems. Zbl 1205.94038
Kirtikar, Siddharth; Palanthandalam-Madapusi, Harish; Zattoni, Elena; Bernstein, Dennis S.
2011
Why are some hysteresis loops shaped like a butterfly? Zbl 1235.93062
Drinčić, Bojana; Tan, Xiaobo; Bernstein, Dennis S.
2011
Arc-length-based Lyapunov tests for convergence and stability with applications to systems having a continuum of equilibria. Zbl 1248.93125
Bhat, Sanjay P.; Bernstein, Dennis S.
2010
Parameter consistency and quadratically constrained errors-in-variables least-squares identification. Zbl 1209.93165
Palanthandalam-Madapusi, Harish J.; van Pelt, Tobin H.; Bernstein, Dennis S.
2010
On the equality between rank and trace of an idempotent matrix. Zbl 1206.15006
Baksalary, Oskar Maria; Bernstein, Dennis S.; Trenkler, Götz
2010
Matrix mathematics. Theory, facts, and formulas. 2nd expanded ed. Zbl 1183.15001
Bernstein, Dennis S.
2009
Modeling and analysis of mass-action kinetics: nonnegativity realizability, reducibility, and semistability. Zbl 1395.93098
Chellaboina, VijaySekhar; Bhat, Sanjay P.; Haddad, Wassim M.; Bernstein, Dennis S.
2009
Asymptotic smooth stabilization of the inverted 3-D pendulum. Zbl 1367.93492
Chaturvedi, Nalin A.; McClamroch, N. Harris; Bernstein, Dennis S.
2009
Nonlinear feedback models of hysteresis. Zbl 1395.93232
Oh, Jinhyoung; Drincic, Bojana; Bernstein, Dennis S.
2009
Matrix pencils and existence conditions for quadratic programming with a sign-indefinite quadratic equality constraint. Zbl 1201.90148
Palanthandalam-Madapusi, Harish J.; Van Pelt, Tobin H.; Bernstein, Dennis S.
2009
State estimation for linear and nonlinear equality-constrained systems. Zbl 1165.93033
Teixeira, Bruno O. S.; Chandrasekar, Jaganath; Tôrres, Leonardo A. B.; Aguirre, Luis A.; Bernstein, Dennis S.
2009
A subspace algorithm for simultaneous identification and input reconstruction. Zbl 1191.93103
Palanthandalam-Madapusi, Harish J.; Bernstein, Dennis S.
2009
Discrete-time adaptive command following and disturbance rejection with unknown exogenous dynamics. Zbl 1367.93308
Hoagg, Jesse B.; Santillo, Mario A.; Bernstein, Dennis S.
2008
Internal model control in the shift and delta domains. Zbl 1367.93231
Hoagg, Jesse B.; Santillo, Mario A.; Bernstein, Dennis S.
2008
Gain-constrained Kalman filtering for linear and nonlinear systems. Zbl 1390.94437
Teixeira, Bruno Otávio Soares; Chandrasekar, Jaganath; Palanthandalam-Madapusi, Harish J.; Tôrres, Leonardo Antônio Borges; Aguirre, Luis Antonio; Bernstein, Dennis S.
2008
Spacecraft tracking using sampled-data Kalman filters: an illustrative application of extended and unscented estimators. Zbl 1395.93548
Teixeira, Bruno O. S.; Santillo, Mario A.; Erwin, R. Scott; Bernstein, Dennis S.
2008
Duhem modeling of friction-induced hysteresis: experimental determination of gearbox stiction. Zbl 1395.93104
Padthe, Ashwani K.; Drincic, Bojana; Oh, Jinhyoung; Rizos, Demosthenis D.; Fassois, Spilios D.; Bernstein, Dennis S.
2008
Stabilization of a 3D axially symmetric pendulum. Zbl 1153.93023
Chaturvedi, N. A.; McClamroch, N. H.; Bernstein, D. S.
2008
Reduced-rank unscented Kalman filtering using Cholesky-based decomposition. Zbl 1148.93349
Chandrasekar, J.; Kim, I. S.; Bernstein, D. S.; Ridley, A. J.
2008
Direct adaptive command following and disturbance rejection for minimum phase systems with unknown relative degree. Zbl 1134.93042
Hoagg, Jesse B.; Bernstein, Dennis S.
2007
Direct adaptive dynamic compensation for minimum phase systems with unknown relative degree. Zbl 1366.93576
Hoagg, Jesse B.; Bernstein, Dennis S.
2007
Extended least-correlation estimates for errors-in-variables non-linear models. Zbl 1140.93498
Jun, B.-E.; Bernstein, D. S.
2007
Kalman filtering with constrained output injection. Zbl 1390.93778
Chandrasekar, J.; Bernstein, D. S.; Barrero, O.; De Moor, B. L. R.
2007
Lyapunov-stable adaptive stabilization of nonlinear time-varying systems with matched uncertainty. Zbl 1124.93050
Hoagg, J. B.; Bernstein, D. S.
2007
Space weather forecasting: identifying periodically switching block-structured models to predict magnetic-field fluctuations. Zbl 1395.93559
Palanthandalam-Madapusi, Harish J.; Bernstein, Dennis S.; Ridley, Aaron J.
2007
Piecewise linear identification for the rate-independent and rate-dependent Duhem hysteresis models. Zbl 1366.93260
Oh, JinHyoung; Bernstein, Dennis S.
2007
Correlation bounds for discrete-time systems with banded dynamics. Zbl 1120.93366
Chandrasekar, Jaganath; Bernstein, Dennis S.
2007
Setpoint tracking with actuator offset and sensor bias: probing the limits of integral control. Zbl 1395.93376
Chandrasekar, Jaganath; Bernstein, Dennis S.
2007
Dimensional analysis of matrices: state-space models and dimensionless units. Zbl 1396.00016
Palanthandalam-Madapusi, Harish J.; Bernstein, Dennis S.; Venugopal, Ravinder
2007
Least-correlation estimates for errors-in-variables models. Zbl 1138.62012
Jun, Byung-Eul; Bernstein, Dennis S.
2006
Data assimilation for magnetohydrodynamics systems. Zbl 1139.76343
Mendoza, O. Barrero; De Moor, B.; Bernstein, D. S.
2006
Geometric homogeneity with applications to finite-time stability. Zbl 1110.34033
Bhat, S. P.; Bernstein, D. S.
2005
Matrix mathematics. Theory, facts, and formulas with application to linear systems theory. Zbl 1075.15001
Bernstein, Dennis S.
2005
Semilinear Duhem model for rate-independent and rate-dependent hysteresis. Zbl 1365.93033
Oh, JinHyoung; Bernstein, Dennis S.
2005
Lyapunov-stable discrete-time model reference adaptive control. Zbl 1127.93337
Akhtar, S.; Bernstein, D. S.
2005
Subspace identification for nonlinear systems with measured-input nonlinearities. Zbl 1086.93011
Lacy, S. L.; Bernstein, D. S.
2005
Adaptive stabilization of linear second-order systems with bounded time-varying coefficients. Zbl 1140.93469
Roup, Alexander V.; Bernstein, Dennis S.
2004
Nontangency-based Lyapunov tests for convergence and stability in systems having a continuum of equilibria. Zbl 1078.34031
Bhat, Sanjay P.; Bernstein, Dennis S.
2003
Subspace identification with guaranteed stability using constrained optimization. Zbl 1364.93162
Lacy, Seth L.; Bernstein, Dennis S.
2003
Limit cycle analysis of the verge and foliot clock escapement using impulsive differential equations and Poincaré maps. Zbl 1052.93044
Roup, Alexander V.; Bernstein, Dennis S.; Nersesov, Sergey G.; Haddad, Wassim M.; Chellaboina, Vijaysekhar
2003
Identification of FIR Wiener systems with unknown, non-invertible, polynomial non-linearities. Zbl 1050.93074
Lacy, Seth L.; Bernstein, Dennis S.
2003
Lyapunov-based backward-horizon adaptive stabilization. Zbl 1033.93061
Venugopal, Ravinder; Rao, Venkatesh G.; Bernstein, Dennis S.
2003
Adaptive stabilization of a class of nonlinear systems with nonparametric uncertainty. Zbl 1015.93056
Roup, Alexander V.; Bernstein, Dennis S.
2001
Nonlinear system identification using Hammerstein and nonlinear feedback models with piecewise linear static maps. Zbl 1039.93015
Van Pelt, Tobin H.; Bernstein, Dennis S.
2001
Adaptive stabilization of nonlinear oscillators using direct adaptive control. Zbl 1017.93095
Hong, Jeongho; Bernstein, Dennis S.
2001
Probability-one homotopy algorithms for solving the coupled Lyapunov equations arising in reduced-order $$H^2/H^\infty$$ modeling, estimation, and control. Zbl 1028.93011
Wang, Y.; Bernstein, D. S.; Watson, L. T.
2001
Finite-time stability of continuous autonomous systems. Zbl 0945.34039
Bhat, Sanjay P.; Bernstein, Dennis S.
2000
A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon. Zbl 0986.93063
Bhat, Sanjay P.; Bernstein, Dennis S.
2000
Induced convolution operator norms of linear dynamical systems. Zbl 1031.93090
Chellaboina, Vijay-Sekhar; Haddad, Wassim M.; Bernstein, Dennis S.; Wilson, David A.
2000
Finite settling time control of the double integrator using a virtual trap-door absorber. Zbl 0972.93026
Bupp, Robert T.; Bernstein, Dennis S.; Chellaboina, Vijaya S.; Haddad, Wassim M.
2000
Global stabilization of systems containing a double integrator using a saturated linear controller. Zbl 0980.93068
Tyan, Feng; Bernstein, Dennis S.
1999
Continuous finite-time stabilization of the translational and rotational double integrators. Zbl 0925.93821
Bhat, Sanjay P.; Bernstein, Dennis S.
1998
Experimental implementation of integrator backstepping and passive nonlinear controllers on the RTAC testbed. Zbl 0925.93352
Bupp, Robert T.; Bernstein, Dennis S.; Coppola, Vincent T.
1998
Robust controller synthesis via shifted parameter-dependent quadratic cost bounds. Zbl 0952.93045
Kapila, Vikram; Haddad, Wassim M.; Erwin, Richard S.; Bernstein, Dennis S.
1998
Fixed-structure robust controller synthesis via decentralized static output feedback. Zbl 0921.93015
Erwin, R. Scott; Sparks, Andrew G.; Bernstein, Dennis S.
1998
Structured matrix norms for robust stability and performance with block-structured uncertainty. Zbl 0954.93008
Chellaboina, Vijaya-Sekhar; Haddad, Wassim M.; Bernstein, Dennis S.
1998
A nonlinear benchmark problem. Special issue. Zbl 0904.00032
Bernstein, Dennis S.
1998
Dynamic output feedback compensation for linear systems with independent amplitude and rate saturations. Zbl 0878.93028
Tyan, Feng; Bernstein, Dennis S.
1997
Robust $$H_ \infty$$ stabilization via parameterized Lyapunov bounds. Zbl 0872.93025
Haddad, Wassim M.; Kapila, Vikram; Bernstein, Dennis S.
1997
Dynamic output feedback compensation for systems with input saturation. Zbl 0878.93029
Tyan, Feng; Bernstein, Dennis S.
1997
Global asymptotic stabilization of a spinning top with torque actuators using stereographic projection. Zbl 0882.93067
Wan, C. J.; Tsiotras, P.; Coppola, V. T.; Bernstein, D. S.
1997
An implicit small gain condition and an upper bound for the real structured singular value. Zbl 0877.93036
Haddad, Wassim M.; Chellaboina, Vijaya-Sekhar; Bernstein, Dennis S.
1997
Example of indeterminacy in classical dynamics. Zbl 0872.70002
Bhat, Sanjay P.; Bernstein, Dennis S.
1997
Optimal rejection of stochastic and deterministic disturbances. Zbl 0883.93023
Sparks, A. G.; Bernstein, D. S.
1997
Globally convergent homotopy algorithms for the combined $$H^2/H^\infty$$ model reduction problem. Zbl 0896.93007
Ge, Yuzhen; Watson, Layne T.; Collins, Emmanuel G. jun.; Bernstein, Dennis S.
1997
Second-order systems with singular mass matrix and an extension of Guyan reduction. Zbl 0857.34003
Bhat, Sanjay P.; Bernstein, Dennis S.
1996
Generalized mixed-$$\mu$$ bounds for real and complex multiple-block uncertainty with internal matrix structure. Zbl 0857.93074
Haddad, Wassim M.; Bernstein, Dennis S.; Chellaboina, Vijaya-Sekhar
1996
The multivariable parabola criterion for robust controller synthesis: A Riccati equation approach. Zbl 0854.93117
1996
Probability-one homotopy algorithms for full- and reduced-order $$H^ 2/ H^ \infty$$ controller synthesis. Zbl 0861.93008
Ge, Yuzhen; Watson, Layne T.; Collins, Emmanuel G. jun.; Bernstein, Dennis S.
1996
A chronological bibliography on saturating actuators. Zbl 0841.93002
Bernstein, Dennis S.; Michel, Anthony N.
1995
Parameter-dependent Lyapunov functions and the Popov criterion in robust analysis and synthesis. Zbl 0821.93063
1995
Special issue on saturating actuators. Zbl 0828.00026
Bernstein, D. S.; Michel, A. N.
1995
Anti-windup compensator synthesis for systems with saturation actuators. Zbl 0831.93033
Tyan, Feng; Bernstein, Dennis S.
1995
Nonlinear feedback control with global stabilization. Zbl 0841.93067
Wan, Chih-Jian; Bernstein, Dennis S.
1995
Global stabilization of the spinning top with mass imbalance. Zbl 0837.93048
Lum, Kai-Yew; Bernstein, Dennis S.; Coppola, Vincent T.
1995
A Popov criterion for uncertain linear multivariable systems. Zbl 0838.93058
Bernstein, Dennis S.; Haddad, Wassim M.; Sparks, Andrew G.
1995
Optimal nonlinear, but continuous, feedback control of systems with saturating actuators. Zbl 0843.93025
Bernstein, Dennis S.
1995
Thermodynamic modelling of interconnected systems. I: Conservative coupling. Zbl 1237.70057
Kishimoto, Y.; Bernstein, D. S.
1995
Energy flow modelling of interconnected structures: A deterministic foundation for statistical energy analysis. Zbl 1046.74521
Kishimoto, Yasuo; Bernstein, Dennis S.; Hall, Steven R.
1995
Global asymptotic stabilization of the spinning top. Zbl 0828.93056
Wan, Chih-Jian; Coppola, Vincent T.; Bernstein, Dennis S.
1995
Thermodynamic modelling of interconnected systems. II: Dissipative coupling. Zbl 1237.70058
Kishimoto, Y.; Bernstein, D. S.
1995
Real structured singular value synthesis using the scaled Popov criterion. Zbl 0841.93012
Sparks, Andrew G.; Bernstein, Dennis S.
1995
The octomorphic criterion for real parameter uncertainty: Real$$-\mu$$ bounds without circles and D, N-scales. Zbl 0877.93081
1995
A double-commutator guaranteed cost bound for robust stability and performance. Zbl 0877.93033
Tyan, Feng; Hall, Steven R.; Bernstein, Dennis S.
1995
Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle, and Popov theorems and their application to robust stability. Part II: Discrete-time theory. Zbl 0806.93045
1994
Parameter-dependent Lyapunov functions and the discrete-time Popov criterion for robust analysis. Zbl 0825.93667
1994
Dissipative $$H_ 2/H_ \infty$$ controller synthesis. Zbl 0807.93022
Haddad, Wassim M.; Bernstein, Dennis S.; Wang, Y. William
1994
Extensions of mixed-$$\mu$$ bounds to monotonic and odd monotonic nonlinearities using absolute stability theory. Zbl 0825.93672
Haddad, Wassim M.; How, Jonathan P.; Hall, Steven R.; Bernstein, Dennis S.
1994
Guardian map approach to robust stability of linear systems with constant real parameter uncertainty. Zbl 0800.93978
Rern, Shuoh; Kabamba, Pierre T.; Bernstein, Dennis S.
1994
Nonlinear controllers for positive real systems with arbitrary input nonlinearities. Zbl 0800.93496
1994
...and 61 more Documents
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#### Cited by 3,280 Authors

 78 Haddad, Wassim Michael 68 Bernstein, Dennis S. 36 Li, Shihua 25 Hui, Qing 24 Du, Haibo 24 Efimov, Denis V. 24 Perruquetti, Wilfrid 23 Šimon Hilscher, Roman 22 Ding, Shihong 21 Polyakov, Andrey 19 Cao, Jinde 17 Lam, James 16 Chellaboina, Vijaysekhar 16 Xie, Lihua 15 Saberi, Ali 14 Jia, Yingmin 14 Moreno, Jaime A. 14 Xiang, Zhengrong 13 Gao, Fangzheng 13 Lin, Zongli 13 Moulay, Emmanuel 13 Šepitka, Peter 13 Stoorvogel, Anton A. 13 Xu, Shengyuan 13 Yu, Xinghuo 12 Shi, Peng 12 Su, Liangjun 11 Chellaboina, Vijaya-Sekhar 11 Petersen, Ian Richard 11 Silvestre, Carlos J. 11 Wang, Zidong 10 Brogliato, Bernard 10 De Koning, Willem L. 10 Hangos, Katalin Mária 10 Shtessel, Yuri B. 10 Szederkényi, Gábor 10 Tian, Bailing 10 Wang, Yijing 10 Wu, Fen 10 Wu, Yuqiang 10 Zhai, Junyong 10 Zheng, Wei Xing 10 Zuo, Zhiqiang 9 Aghababa, Mohammad Pourmahmood 9 Fridman, Leonid M. 9 Hong, Yiguang 9 Nersesov, Sergey G. 9 Song, Yongduan 9 Zhao, Lin 8 Chen, Bing 8 Duan, Guangren 8 Garcia, Germain 8 Hayakawa, Tomohisa 8 Hoagg, Jesse B. 8 Iwasaki, Tetsuya 8 Kogan, Mark Mikhailovich 8 Lin, Chong 8 Logemann, Hartmut 8 Sun, Zongyao 8 Teel, Andrew Richard 8 Tian, Yongge 8 van Willigenburg, L. Gerard 8 Wang, Long 8 Yang, Guanghong 8 Yucelen, Tansel 8 Zemánek, Petr 8 Zhang, Qingling 8 Zuo, Zongyu 7 Amato, Francesco 7 Bernuau, Emmanuel 7 Bhat, Sanjay P. 7 Chen, Michael Z. Q. 7 Collins, Emmanuel G. jun. 7 Fu, Junjie 7 Huang, Shipei 7 Jammazi, Chaker 7 Khoo, Suiyang 7 Krstić, Miroslav 7 L’Afflitto, Andrea 7 Lin, Xiangze 7 Shen, Yanjun 7 Skelton, Robert E. 7 Tarbouriech, Sophie 7 Wang, Fang 7 Wang, Jinzhi 7 Wang, Xu 7 Wen, Changyun 7 Xie, Xuejun 7 Zong, Qun 6 Balandin, Dmitriĭ Vladimirovich 6 Basin, Michael V. 6 Chen, Chih-Chiang 6 Cheng, Yingying 6 Cunha, Rita 6 de Souza, Carlos Emanuel 6 Goebel, Rafal 6 Gugercin, Serkan 6 Gui, Haichao 6 Halevi, Yoram 6 Ho, Daniel W. C. ...and 3,180 more Authors
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#### Cited in 228 Serials

 368 Automatica 222 International Journal of Control 179 Journal of the Franklin Institute 169 Systems & Control Letters 84 International Journal of Robust and Nonlinear Control 81 Nonlinear Dynamics 59 Mathematical Problems in Engineering 51 European Journal of Control 50 Linear Algebra and its Applications 49 Applied Mathematics and Computation 45 International Journal of Systems Science 33 International Journal of Systems Science. Principles and Applications of Systems and Integration 31 Asian Journal of Control 26 Complexity 23 Automation and Remote Control 22 Journal of Optimization Theory and Applications 22 SIAM Journal on Control and Optimization 20 International Journal of Adaptive Control and Signal Processing 17 MCSS. Mathematics of Control, Signals, and Systems 17 Communications in Nonlinear Science and Numerical Simulation 16 Journal of Mathematical Analysis and Applications 16 Circuits, Systems, and Signal Processing 15 Journal of Econometrics 15 Abstract and Applied Analysis 15 Nonlinear Analysis. Hybrid Systems 14 Journal of Computational and Applied Mathematics 12 Information Sciences 12 Kybernetika 10 Journal of Differential Equations 10 Optimal Control Applications & Methods 10 Journal of Mathematical Chemistry 10 Chaos 10 Advances in Difference Equations 9 Chaos, Solitons and Fractals 9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 Linear and Multilinear Algebra 8 Neural Networks 8 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 8 Multibody System Dynamics 8 Journal of Systems Science and Complexity 7 Journal of Computer and Systems Sciences International 7 Journal of Vibration and Control 7 Nonlinear Analysis. Real World Applications 6 Computers & Mathematics with Applications 6 International Journal of Applied Mathematics and Computer Science 6 Journal of Control Science and Engineering 6 Nonlinear Analysis. Theory, Methods & Applications 5 Fuzzy Sets and Systems 5 Optimization 5 Applied Mathematics Letters 5 SIAM Journal on Matrix Analysis and Applications 5 Applied Mathematical Modelling 5 International Journal of Computer Mathematics 5 Mathematical Programming. Series A. Series B 5 Computational and Applied Mathematics 5 Discrete Dynamics in Nature and Society 5 Journal of Applied Mathematics and Computing 5 Journal of Control Theory and Applications 4 Journal of Mathematical Physics 4 International Journal for Numerical Methods in Engineering 4 Physica D 4 Machine Learning 4 Journal of Difference Equations and Applications 4 ELA. The Electronic Journal of Linear Algebra 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 Soft Computing 4 Econometric Theory 4 Entropy 4 Science in China. Series F 3 Journal of Mathematical Biology 3 Applied Mathematics and Optimization 3 Journal of Multivariate Analysis 3 Applied Numerical Mathematics 3 Numerical Algorithms 3 SIAM Journal on Optimization 3 Computational Optimization and Applications 3 Journal of Mathematical Sciences (New York) 3 Doklady Mathematics 3 Journal of Inequalities and Applications 3 Journal of Applied Mathematics 3 Electronic Journal of Statistics 3 Journal of Theoretical Biology 3 Control Theory and Technology 2 Computer Methods in Applied Mechanics and Engineering 2 Discrete Mathematics 2 International Journal of Engineering Science 2 Journal of Statistical Physics 2 Mathematical Methods in the Applied Sciences 2 Physica A 2 Calcolo 2 Mathematics and Computers in Simulation 2 Mechanics Research Communications 2 Applied Mathematics and Mechanics. (English Edition) 2 Acta Applicandae Mathematicae 2 European Journal of Applied Mathematics 2 Journal of Global Optimization 2 Dynamics and Control 2 SIAM Journal on Applied Mathematics 2 SIAM Review 2 Computational Statistics and Data Analysis ...and 128 more Serials
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#### Cited in 50 Fields

 1,782 Systems theory; control (93-XX) 216 Ordinary differential equations (34-XX) 162 Linear and multilinear algebra; matrix theory (15-XX) 123 Calculus of variations and optimal control; optimization (49-XX) 121 Mechanics of particles and systems (70-XX) 108 Computer science (68-XX) 103 Operations research, mathematical programming (90-XX) 90 Numerical analysis (65-XX) 85 Probability theory and stochastic processes (60-XX) 81 Dynamical systems and ergodic theory (37-XX) 76 Biology and other natural sciences (92-XX) 49 Statistics (62-XX) 42 Information and communication theory, circuits (94-XX) 37 Combinatorics (05-XX) 36 Partial differential equations (35-XX) 27 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 25 Mechanics of deformable solids (74-XX) 23 Operator theory (47-XX) 19 Difference and functional equations (39-XX) 18 Quantum theory (81-XX) 12 Functional analysis (46-XX) 11 Optics, electromagnetic theory (78-XX) 9 Approximations and expansions (41-XX) 9 Classical thermodynamics, heat transfer (80-XX) 9 Statistical mechanics, structure of matter (82-XX) 6 Fluid mechanics (76-XX) 5 Associative rings and algebras (16-XX) 4 Mathematical logic and foundations (03-XX) 4 Real functions (26-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 General and overarching topics; collections (00-XX) 3 Number theory (11-XX) 3 Functions of a complex variable (30-XX) 2 Commutative algebra (13-XX) 2 Algebraic geometry (14-XX) 2 Nonassociative rings and algebras (17-XX) 2 Group theory and generalizations (20-XX) 2 Special functions (33-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral transforms, operational calculus (44-XX) 2 Integral equations (45-XX) 2 Geometry (51-XX) 2 Differential geometry (53-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX) 1 Sequences, series, summability (40-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX)

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