Stability criteria for uncertain stochastic dynamic systems with time-varying delays. (English) Zbl 1213.93201

Summary: The problem of delay-dependent stability for uncertain stochastic dynamic systems with time-varying delay is considered. Based on the Lyapunov stability theory, improved delay-dependent stability criteria for the system are established in terms of linear matrix inequalities. Three numerical examples are given to show the effectiveness of the proposed method.


93E15 Stochastic stability in control theory
93E03 Stochastic systems in control theory (general)
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
Full Text: DOI


[1] Hale, Introduction to Functional Differential Equations (1993) · Zbl 0787.34002
[2] Kolmanovskii, Applied Theory of Functional Differential Equations (1992) · Zbl 0840.34084
[3] Kwon, On stability criteria for uncertain delay-differential systems of neutral type with time-varying delays, Applied Mathematics and Computation 197 pp 864– (2009) · Zbl 1144.34052
[4] Kwon, On robust stability criterion for dynamic systems with time-varying delays and nonlinear perturbations, Applied Mathematics and Computation 203 pp 937– (2008) · Zbl 1168.34354
[5] Park, Delay-dependent guaranteed cost stabilization criterion for neutral-delay-differential systems: matrix inequality approach, Computers and Mathematics with Applications 47 pp 1507– (2004) · Zbl 1070.34106
[6] Cao, Boundedness and stability for Cohen-Grossberg neural network with time-varying delays, Journal of Mathematical Analysis and Applications 296 pp 665– (2004) · Zbl 1044.92001
[7] Kwon, On improved delay-dependent stability criterion of certain neutral differential equations, Applied Mathematics and Computation 199 pp 385– (2008) · Zbl 1146.34328
[8] Li, Delay-range-dependent robust stability and stabilization for uncertain systems with time-varying delay, International Journal of Robust and Nonlinear Control 18 pp 1372– (2008) · Zbl 1298.93263
[9] Yue, Delay-dependent robust stability of stochastic systems with time delay and nonlinear uncertainties, Electronics Letters 37 pp 992– (2001) · Zbl 1190.93095
[10] Xu, A new LMI condition for delay dependent robust stability of stochastic time-delay systems, Asian Journal of Control 7 pp 419– (2005)
[11] Yang, New delay-dependent stability criterion for stochastic systems with time delays, IET Control Theory and Applications 2 pp 966– (2008)
[12] Yan, Delay-dependent robust stability criteria of uncertain stochastic systems with time-varying delay, Chaos Solitons Fractals 40 pp 1668– (2009) · Zbl 1198.93171
[13] Gu K An integral inequality in the stability problem of time-delay systems 2805 2810
[14] Boyd, Linear Matrix Inequalities in System and Control Theory (1994) · Zbl 0816.93004
[15] Khasminskii, Stochastic Stability of Differential Equations (1980) · Zbl 1259.60058
[16] Arnold, Stochastic Differential Equations: Theory and Applications (1972)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.