zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Delay-dependent stability of reset systems. (English) Zbl 1214.93072
Summary: This work presents results on the stability of time-delay systems under reset control. The case of delay-dependent stability is addressed, by developing a generalization of previous stability results for reset systems without delay, and also a generalization of the delay-independent case. The stability results are derived by using appropriate Lyapunov-Krasovskii functionals, obtaining LMI (Linear Matrix Inequality) conditions and showing connections with passivity and positive realness. The stability conditions guarantee that the reset action does not destabilize the base LTI (Linear Time Invariant) system. Several interpretations are given for these conditions in terms of impulsive control, which provide insights into the potentials of reset control.

MSC:
93D05Lyapunov and other classical stabilities of control systems
93C30Control systems governed by other functional relations
93B35Sensitivity (robustness) of control systems
WorldCat.org
Full Text: DOI
References:
[1] A\ring ström, K. J.: Limitations on control system performance, European journal of control 6, 2-20 (2000) · Zbl 1167.93348
[2] Bainov, D. D.; Simeonov: Systems with impulse effect: stability, theory and applications, (1989) · Zbl 0683.34032
[3] Baños, A.; Barreiro, A.: Delay-independent stability of reset systems, IEEE transactions on automatic control, 341-346 (2009)
[4] Baños, A., Carrasco, J., & Barreiro, A. (2007). Reset-times dependent stability of reset control with unstable base systems. In Proceedings of the IEEE Int. Symp. on Industrial Electronics (ISIE), Vigo, Spain, June 4-7
[5] Beker, O.; Hollot, C. V.; Chait, Y.; Han, H.: Fundamental properties of reset control systems, Automatica 40, 905-915 (2004) · Zbl 1068.93050 · doi:10.1016/j.automatica.2004.01.004
[6] Carrasco, J., Baños, A., & van der Schaft, A. (2008). A passivity approach to reset control on nonlinear systems, IEEE Ind. Electr. Conference (IECON), Orlando, Florida, 10-13 November
[7] Chen, T.; Francis, B. A.: Input-output stability of sampled data systems, IEEE transactions on automatic control 36, No. 1 (1991) · Zbl 0723.93059 · doi:10.1109/9.62267
[8] Clegg, J. C.: A nonlinear integrator for servomechanism, Transactions a.i.e.e.m, part II 77, 41-42 (1958)
[9] De La Sen, M.; Luo, N.: A note on the stability of linear time-delay systems with impulsive inputs, IEEE transactions on circuits and systems 50, No. 1, 149-152 (2003)
[10] Fernández, A., Barreiro, A., Baños, A., & Carrasco, J. (2008). Reset control for passive teleoperation. IEEE Ind. Electr. Conf. (IECON), Orlando, Florida, 10-13 November 2008
[11] Hespanha, J. P.; Liberzon, D.; Teel, A. R.: Lyapunov conditions for input to state stability of impulsive systems, Automatica 44, 2735-2744 (2008) · Zbl 1152.93050 · doi:10.1016/j.automatica.2008.03.021
[12] Horowitz, I. M.; Rosenbaum: Nonlinear design for cost of feedback reduction in systems with large parameter uncertainty, International journal of control 24, No. 6, 977-1001 (1975) · Zbl 0312.93019 · doi:10.1080/00207177508922051
[13] Gu, K.; Kharitonov, V. L.; Chen, J.: Stability of time-delay systems, (2003) · Zbl 1039.34067
[14] Guo, Y., Wang, Y., Zheng, J., & Xie, L. (2007). Stability analysis, design and application of reset control systems. In Proceedings of the IEEE Int. Conf. on Control and Automation, Guangzhou, China, May 30-June 1, 2007
[15] Haddad, W. M.; Nersesov, S. G.; Chellaboina, V. S.: Energy-based control for hybrid port-controlled Hamiltonian systems, Automatica 39, 1425-1435 (2003) · Zbl 1034.93036 · doi:10.1016/S0005-1098(03)00113-4
[16] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S.: Theory of impulsive differential equations, (1989) · Zbl 0718.34011
[17] Liu, X.; Ballinger, G.: Uniform asymptotic stability of impulsive delay differential equations, Computers and mathematics with applications 41, 903-915 (2001) · Zbl 0989.34061 · doi:10.1016/S0898-1221(00)00328-X
[18] Liu, X.; Shen, X.; Zhang, Y.; Wang, Q.: Stability criteria for impulsive systems with time delay and unstable system matrices, IEEE transactions on circuits and sytems 54, No. 10 (2007)
[19] Liu, X.; Wang, Q.: Stability of nontrivial solution of delay differential equations with state-dependent impulses, Applied mathematics and computation 174, 271-288 (2006) · Zbl 1100.34059 · doi:10.1016/j.amc.2005.03.028
[20] Krishman, K. R.; Horowitz, I. M.: Synthesis of a nonlinear feedback system with significant plant-ignorance for prescribed system tolerances, International journal of control 19, No. 4, 689-706 (1974) · Zbl 0276.93019 · doi:10.1080/00207177408932666
[21] Nešić, D.; Zaccarian, L.; Teel, A. R.: Stability properties of reset systems, Automatica 44, 2019-2026 (2005) · Zbl 1283.93213
[22] Park, P.: A delay-dependent stability criterion for systems with uncertain time-invariant delays, IEEE transactions on automatic control 44, 876-877 (1999) · Zbl 0957.34069 · doi:10.1109/9.754838
[23] Yang, T.: Impulsive control theory, Lecture notes in control and information sciences 272 (2001)
[24] Zhang, J.; Knospe, C. R.; Tsiotras, P.: Stability of time-delay systems: equivalence between Lyapunov and scaled small-gain conditions’, IEEE transactions on automatic control 46, 482-486 (2001) · Zbl 1056.93598 · doi:10.1109/9.911428