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)
Robust stability analysis of uncertain systems with two additive time-varying delay components. (English) Zbl 1173.93024
Summary: This paper is concerned with stability analysis for uncertain systems. The systems are based on a new time-delay model proposed recently, which contains multiple successive delay components in the state. The relationship between the time-varying delay and its upper bound is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some less conservative stability criteria are established for systems with two successive delay components and parameter uncertainties. Numerical examples show that the proposed criteria are effective and are an improvement over some existing results in the literature.
MSC:
93D09Robust stability of control systems
93C41Control problems with incomplete information
93C23Systems governed by functional-differential equations
93C15Control systems governed by ODE
15A39Linear inequalities of matrices
Software:
LMI toolbox
References:
[1]Peng, C.; Tian, Y.: Delay-dependent robust stability criteria for uncertain systems with interval time-varying delay, J. comput. Appl. math. 214, No. 2, 480-494 (2008) · Zbl 1136.93437 · doi:10.1016/j.cam.2007.03.009
[2]Peng, C.; Tian, Y.: Networked H control of linear systems with state quantization, Inform. sci. 177, No. 24, 5763-5774 (2007) · Zbl 1126.93338 · doi:10.1016/j.ins.2007.05.025
[3]Fridman, E.; Shaked, U.: An improved stabilization method for linear time-delay systems, IEEE trans. Automat. control 47, No. 11, 1931-1937 (2002)
[4]Fridman, E.; Shaked, U.: Delay-dependent stability and H control: constant and time-varying delays, Int. J. Control 76, No. 1, 48-60 (2003) · Zbl 1023.93032 · doi:10.1080/0020717021000049151
[5]Gu, K.; Kharitonov, V. L.; Chen, J.: Stability of time-delay systems, (2003)
[6]He, Y.; Wang, Q.; Lin, C.; Wu, M.: Delay-range-dependent stability for systems with time-varying delay, Automatica 43, No. 2, 371-376 (2007) · Zbl 1111.93073 · doi:10.1016/j.automatica.2006.08.015
[7]He, Y.; Wang, Q.; Xie, L.; Lin, C.: Further improvement of free-weighting matrices technique for systems with time-varying delay, IEEE trans. Automat. control 52, No. 2, 293-299 (2007)
[8]He, Y.; Wu, M.; J., H. She; Liu, G. P.: Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties, IEEE trans. Automat. control 49, No. 5, 828-832 (2004)
[9]Jing, X.; Tan, D.; Wang, Y.: An LMI approach to stability of systems with severe time-delay, IEEE trans. Automat. control 49, No. 7, 1192-1195 (2004)
[10]Kim, J.: Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty, IEEE trans. Automat. control 46, No. 5, 789-792 (2001) · Zbl 1008.93056 · doi:10.1109/9.920802
[11]Y. Lee, Y. Moon, W. Kwon, K. Lee, Delay-dependent robust Hnbsp; control for uncertain systems with time-varying state-delay, in: Proceedings of the 40th Conference on Decision Control, vol. 4, Orlando, FL, 2001, pp. 3208 – 3213.
[12]Lin, C.; Wang, Q.; Lee, T.: A less conservative robust stability test for linear uncertain time-delay systems, IEEE trans. Automat. control 51, No. 1, 87-91 (2006)
[13]Xu, S.; Lam, J.: Improved delay-dependent stability criteria for time-delay systems, IEEE trans. Automat. control 50, No. 3, 384-387 (2005)
[14]Moon, Y.; Park, P.; Kwon, W.; Lee, Y.: Delay-dependent robust stabilization of uncertain state-delayed systems, Int. J. Control 74, No. 14, 1447-1455 (2001) · Zbl 1023.93055 · doi:10.1080/00207170110067116
[15]Wu, M.; He, Y.; She, J.; Liu, G.: Delay-dependent criteria for robust stability of time-varying delay systems, Automatica 40, No. 8, 1435-1439 (2004) · Zbl 1059.93108 · doi:10.1016/j.automatica.2004.03.004
[16]H. Yan, X. Huang, H. Zhang, M. Wang, Delay-dependent robust stability criteria of uncertain stochastic systems with time-varying delay, Chaos, Solitons amp; Fractals, in press, doi:10.1016/j.chaos.2007.09.049. · Zbl 1198.93171 · doi:10.1016/j.chaos.2007.09.049
[17]Zhang, Z.; Li, C.; Liao, X.: Delay-dependent robust stability analysis for interval linear time-variant systems with delays and application to delayed neural networks, Neurocomputing 70, No. 16 – 18, 2980-2995 (2007)
[18]Corless, M.: Guaranteed rates of exponential convergence for exponential convergence for uncertain system, J. opt. Theor. appl. 67, No. 3, 481-494 (1990) · Zbl 0682.93040 · doi:10.1007/BF00939420
[19]Karimi, H. R.: Robust dynamic parameter-dependent output feedback control of uncertain parameter-dependent state-delayed systems, Nonlinear dynam. Syst. theor. 6, No. 2, 143-158 (2006) · Zbl 1135.93027
[20]Lou, X. Y.; Cui, B. T.: Robust stability for nonlinear uncertain neural networks with delay, Nonlinear dynam. Syst. theor. 7, No. 4, 369-378 (2007) · Zbl 1138.93395
[21]Lam, J.; Gao, H.; Wang, C.: Stability analysis for continuous systems with two additive time-varying delay components, Syst. control lett. 56, No. 1, 16-24 (2007) · Zbl 1120.93362 · doi:10.1016/j.sysconle.2006.07.005
[22]Gao, H.; Chen, T.; Lam, J.: A new delay system approach to network-based control, Automatica 44, No. 1, 39-52 (2008) · Zbl 1138.93375 · doi:10.1016/j.automatica.2007.04.020
[23]He, Y.; Liu, G. P.; Rees, D.; Wu, M.: Stability analysis for neural networks with time-varying interval delay, IEEE trans. Neural networks 18, No. 6, 1850-1854 (2007)
[24]Gahinet, P.; Nemirovskii, A.; Laub, A.; Chilali, M.: LMI control toolbox user’s guide, (1995)
[25]Ladyzhenskaya, O. A.: Boundary value problems of mathematical physics. Moscow: nauka 1973. English transl. The boundary value problems of mathematical physics, (1985)
[26]Hale, J. K.; Lunel, S. M. Verduyn: Introduction of functional differential equations, (1993)