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)
Exponential stability results for uncertain neutral systems with interval time-varying delays and Markovian jumping parameters. (English) Zbl 1197.34160
Summary: This paper deals with the global exponential stability analysis of neutral systems with Markovian jumping parameters and interval time-varying delays. The time-varying delay is assumed to belong to an interval, which means that the lower and upper bounds of interval time-varying delays are available. A new global exponential stability condition is derived in terms of linear matrix inequalities (LMI) by constructing new Lyapunov-Krasovskii functionals via generalized eigenvalue problems. The stability criteria are formulated in the form of LMIs, which can be easily checked in practice by the Matlab LMI control toolbox. Two numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.
MSC:
34K50Stochastic functional-differential equations
34K40Neutral functional-differential equations
34K20Stability theory of functional-differential equations
Software:
Matlab
References:
[1]Blair, W. P.; Sworder, D. D.: Feedback control of a class of linear discrete systems with jump parameters and quadratic cost criteria, International journal of control 21, 833-841 (1975) · Zbl 0303.93084 · doi:10.1080/00207177508922037
[2]Sworder, D. D.; Rogers, R. O.: An LQG solution to a control problem with solar thermal receiver, IEEE transactions on automatic control 28, 971-978 (1983)
[3]Athans, M.: Command and control (C2) theroy: a challenge to control science, IEEE transactions on automatic control 32, 286-293 (1987)
[4]Hale, J. K.; Lunel, S. M. Verduyn: Introduction to functional differential equations, (1993)
[5]Lien, C. H.; Chen, J. D.: Discrete-delay-independent, discrete-delay-dependent criteria for a class of neutral systems, Journal of dynamic systems, measurement and control 125, 33-41 (2003)
[6]Park, J. H.: Novel robust stability criterion for a class of neutral systems with mixed delays and nonlinear perturbations, Applied mathematics and computation 161, 413-421 (2005) · Zbl 1065.34076 · doi:10.1016/j.amc.2003.12.036
[7]Park, J. H.: Robust stabilization for dynamic systems with multiple time-varying delays and nonlinear uncertainties, Journal of optimization theory and applications 108, 155-174 (2001) · Zbl 0981.93069 · doi:10.1023/A:1026470106976
[8]Kwon, O. M.; Park, J. H.: Delay-range-dependent stabilization of uncertain dynamic systems with interval time-varying delays, Applied mathematics and computation 208, 58-68 (2009) · Zbl 1170.34054 · doi:10.1016/j.amc.2008.11.010
[9]Kwon, O. M.; Park, J. H.; Lee, S. M.: On robust stability for uncertain neural networks with interval time-varying delays, IET control theory and applications 2, 625-634 (2008)
[10]Han, Q. L.: On stability of linear neutral systems with mixed time delays: a discretized Lyapunov functional approach, Automatica 41, 1209-1218 (2005) · Zbl 1091.34041 · doi:10.1016/j.automatica.2005.01.014
[11]Park, J. H.: Stability criterion for neutral differential systems with mixed multiple time-varying delay arguments, Mathematics and computers in simulation 59, 401-412 (2002) · Zbl 1006.34072 · doi:10.1016/S0378-4754(01)00420-7
[12]Han, Q. L.: A new delay-dependent stability criterion for linear neutral systems with norm-bounded uncertainties in all system matrices, International journal of systems science 36, 469-475 (2005) · Zbl 1093.34037 · doi:10.1080/00207720500157437
[13]He, Y.; Wu, M.; She, J. H.; Liu, G. P.: Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays, Systems and control letters 51, 57-65 (2004) · Zbl 1157.93467 · doi:10.1016/S0167-6911(03)00207-X
[14]Xu, S.; Lam, J.; Zou, Y.: Further results on delay-dependent robust stability conditions of uncertain neutral systems, International journal of robust and nonlinear control 15, 233-246 (2005) · Zbl 1078.93055 · doi:10.1002/rnc.983
[15]Xu, S.; Lam, J.: A survey of linear matrix inequality techniques in stability analysis of delay systems, International journal of systems science 39, 1095-1113 (2008) · Zbl 1156.93382 · doi:10.1080/00207720802300370
[16]Xu, S.; Feng, G.: Improved robust absolute stability criteria for uncertain time-delay systems, IET control theory and applications 1, 1630-1637 (2007)
[17]He, Y.; Wang, Q. G.; Lin, C.; Wu, M.: Augmented Lyapunov functional and delay-dependent stability criteria for neutral systems, International journal of robust and nonlinear control 15, 923-933 (2005) · Zbl 1124.34049 · doi:10.1002/rnc.1039
[18]Yu, K. W.; Lien, C. H.: Stability criteria for uncertain neutral systems with interval time-varying delays, Chaos, solitons, fractals 38, 650-657 (2008) · Zbl 1146.93366 · doi:10.1016/j.chaos.2007.01.002
[19]Parlakci, M. N. A.: Delay-dependent robust stability criteria for uncertain neutral systems with mixed time-varying discrete and neutral delays, Asian journal of control 9, 411-421 (2008)
[20]Zhang, J.; Shi, P.; Qiu, J.: Robust stability criteria for uncertain neutral system with time delay and nonlinear uncertainties, Chaos, solitons, fractals 38, 160-167 (2008) · Zbl 1142.93402 · doi:10.1016/j.chaos.2006.10.068
[21]Liu, M.: Stability analysis of neutral-type nonlinear delayed systems: an LMI approach, Journal of zhejiang university science 7, 237-244 (2006) · Zbl 1134.34328 · doi:10.1631/jzus.2006.AS0237
[22]Shen, C. C.; Zhong, S. M.: New delay-dependent robust stability criterion for uncertain neutral systems with time-varying delay and nonlinear uncertainties, Chaos, solitons, fractals 40, 2277-2285 (2009) · Zbl 1198.93164 · doi:10.1016/j.chaos.2007.10.020
[23]Karimi, H. R.; Zapateiro, M.; Luo, N.: Stability analysis and control synthesis of neutral systems with time-varying delays and nonlinear uncertainties, Chaos, solitons, fractals 42, 595-603 (2009) · Zbl 1198.93180 · doi:10.1016/j.chaos.2009.01.028
[24]Krasovskii, N. N.; Lidskii, E. A.: Analysis design of controller in systems with random attributes, part I, Automatic remote control 22, 1021-1025 (1961)
[25]Sun, X. M.; Zhao, J.; Hill, D. J.: Stability and gain analysis for switched delay systems: a delay-dependent method, Automatica 42, 1769-1774 (2006) · Zbl 1114.93086 · doi:10.1016/j.automatica.2006.05.007
[26]Sun, X. M.; Wang, W.; Zhao, J.: Stability analysis for linear switched systems with time-varying delay, IEEE transactions on system man cybernetics B 38, 528-533 (2008)
[27]Xu, S.; Lam, J.; Mao, X.: Delay-dependent H control and filtering for uncertain Markovian jump systems with time-varying delays, IEEE transactions on circuits and systems-I: regular papers 54, 2070-2077 (2007)
[28]Mariton, M.: Jump linear systems in automatic control, (1990)
[29]Chen, B.; Li, H.; Shi, P.; Lin, C.; Zhou, Q.: Delay-dependent stability analysis and controller synthesis for Markovian jump systems with state and input delays, Information sciences 179, 2851-2860 (2009) · Zbl 1165.93341 · doi:10.1016/j.ins.2009.04.006
[30]P. Gahinet, A. Nemirovski, A. Laub, M. Chilali, LMI Control Toolbox User’s Guide, The Mathworks, MA, 1995.
[31]He, S.; Liu, F.: Exponential stability for uncertain neutral systems with Markov jumps, Journal of control theory and applications 7, 35-40 (2009) · Zbl 1199.93273 · doi:10.1007/s11768-009-7220-5
[32]Bellen, A.; Guglielmi, N.; Ruehli, A. E.: Methods for linear systems of circuit delay differential equations of neutral type, IEEE transactions on circuits and system 46, 212-215 (1999) · Zbl 0952.94015 · doi:10.1109/81.739268
[33]D. Yue, Q.L. Han, A delay-dependent stability criterion of neutral systems and its application to a partial element equivalent circuit model, in: Proceedings of the 2004 American Control Conference, IEEE Press, Piscataway, 2004, pp. 5438 – 5442.
[34]Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in systems and control theory, SIAM studies in applied mathematics (1994)