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 analysis for neutral switched systems with interval time-varying mixed delays and nonlinear perturbations. (English) Zbl 1238.93090
Summary: This paper is concerned with the problem of exponential stability for uncertain neutral switched systems with interval time-varying mixed delays and nonlinear perturbations. By using the average dwell time approach and the piecewise Lyapunov functional technique, some sufficient conditions are first proposed in terms of a set of Linear Matrix Inequalities (LMIs), to guarantee the robustly exponential stability for the uncertain neutral switched systems, where the decay estimate is explicitly given to quantify the convergence rate. Three numerical examples finally illustrate the effectiveness of the proposed method.
MSC:
93D20Asymptotic stability of control systems
93C15Control systems governed by ODE
34K10Boundary value problems for functional-differential equations
93C73Perturbations in control systems
References:
[1]Fridman, E.; Shaked, U.: An improved stabilization method for linear time-delay systems, IEEE trans. Automat. control 47, 1931-1937 (2003)
[2]Wu, M.; He, Y.; She, J.; Liu, G.: Delay-dependent criteria for robust stability of time-varying delay systems, Automatica 40, 1435-1439 (2004) · Zbl 1059.93108 · doi:10.1016/j.automatica.2004.03.004
[3]Liu, X.; Zhang, H.: New stability criterion of uncertain systems with time-varying delay, Chaos solitons fractals 26, 1343-1348 (2005) · Zbl 1075.34072 · doi:10.1016/j.chaos.2005.04.002
[4]He, Y.; Wang, Q.; Lin, C.; Wu, M.: Delay-range-dependent stability for systems with time-varying delay, Automatica 43, 371-376 (2007) · Zbl 1111.93073 · doi:10.1016/j.automatica.2006.08.015
[5]Shao, H.: New delay-dependent stability criteria for systems with interval delays, Automatica 45, 744-749 (2009) · Zbl 1168.93387 · doi:10.1016/j.automatica.2008.09.010
[6]Park, J. H.: Novel robust stability criterion for a class of neutral systems with mixed delays and nonlinear perturbations, Appl. math. Comput. 161, 413-421 (2005) · Zbl 1065.34076 · doi:10.1016/j.amc.2003.12.036
[7]Yang, B.; Wang, J.; Pan, X.; Zhong, C.: Delay-dependent criteria for robust stability of linear neutral systems with time-varying delay and nonlinear perturbations, Internat. J. Systems sci. 38, 511-518 (2007) · Zbl 1126.93046 · doi:10.1080/00207720701393302
[8]Zhang, J.; Peng, S.; Qiu, J.: Robust stability criteria for uncertain neutral system with time delay and nonlinear uncertainties, Chaos solitons fractals 28, 160-167 (2008) · Zbl 1142.93402 · doi:10.1016/j.chaos.2006.10.068
[9]Chen, Y.; Xue, A. K.; Lu, R.; Zhou, S. -S.: On robustly exponential stability of uncertain neutral systems with time-varying delays and nonlinear perturbations, Nonlinear anal. 68, 2464-2470 (2008) · Zbl 1147.34352 · doi:10.1016/j.na.2007.01.070
[10]Fang, Q.; Cui, B. T.; Yan, J.: Further results on robust stability of neutral system with mixed time-varying delays and nonlinear perturbations, Nonlinear anal. RWA. 11, No. 2, 895-906 (2011) · Zbl 1187.37124 · doi:10.1016/j.nonrwa.2009.01.032
[11]Liu, J.; Liu, X.; Xie, W. C.: Delay-dependent robust control for uncertain switched systems with time-delay, Nonlinear anal. Hybrid syst. 2, 81-95 (2008) · Zbl 1157.93362 · doi:10.1016/j.nahs.2007.04.001
[12]Y.G. Sun, L. Wang, G. Xie, Stability of switched systems with time-varying delays: delay-dependent common Lyapunov functional approach, in: Proc. Amer. Control Conf., vol. 5, 2006, pp. 1544–1549.
[13]C.H. Wang, L.X. Zhang, H.J. Gao, L.G. Wu, Delay-dependent stability and stabilization of a class of linear switched time-varying delay systems, in: Proc. 4th Int. Conf. Mach. Learn. Cybern., Guangzhou, 2005, pp. 18–21.
[14]Lien, C. H.; Yu, K. W.; Chung, Y. J.; Lin, Y. F.: Exponential stability analysis for uncertain switched neutral systems with interval-time-varying state delay, Nonlinear anal. Hybrid syst. 3, 334-342 (2009) · Zbl 1192.34085 · doi:10.1016/j.nahs.2009.02.010
[15]J. Hespanha, A.S. Morse, Stability of switched systems with average dwell-time, in: Proc. the 38th Conf. on Decision and Contr., 1999, pp. 2655–2660.
[16]Sun, X. M.; Zhao, J.; Hill, D. J.: Stability and L2-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
[17]Liu, D.; Zhong, S.; Liu, X.; Huang, Y.: Stability analysis for uncertain switched neutral systems with discrete time-varying delay: a delay-dependent method, Math. comput. Simul. (2008)
[18]Han, Q. L.: Absolute stability of time-delay systems with sector-bounded nonlinearity, Automatica 41, 2171-2176 (2005) · Zbl 1100.93519 · doi:10.1016/j.automatica.2005.08.005
[19]Petersen, I. R.; Hollot, C. V.: A Riccati equation approach to the stabilization of uncertain linear systems, Automatica 22, 397-411 (1986) · Zbl 0602.93055 · doi:10.1016/0005-1098(86)90045-2
[20]Wu, L. G.; Wang, Z. D.: Guaranteed cost control of switched systems with neutral delay via dynamic output feedback, Internat. J. Systems sci. 40, No. 7, 717-728 (2009)
[21]Yan, P.; Özbay, H.: Stability analysis of switched time delay systems, SIAM J. Control optim. 47, No. 2, 936-949 (2008) · Zbl 1157.93462 · doi:10.1137/060668262