This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation and introducing free weighting matrices, a new type of Lyapunov-Krasovskii functional is constructed based on linear matrix inequalities (LMIs), and some new delay-dependent criteria are obtained. These criteria include the delay-independent/ratedependent and delay-dependent/rate-independent exponential stability criteria. These new criteria are less conservative than existing ones. Numerical examples demonstrate that these new criteria are effective and are an improvement over existing ones.
Stochastic system Exponential stability in mean square Time-varying state delay Delay-dependent criteria Linear matrix inequality (LMI)
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D. Yue, S. Won. Delay-dependent robust stability of stochastic systems with time delay and nonlinear uncertainties[J]. Electronics Letters, 2001, 37(15): 992–993.CrossRefGoogle Scholar
C. Lu, J. Tsai. An LMI-Based approach for robust stabilization of uncertain stochastic systems with time-varying delays[J]. IEEE Transactions on Automatic Control, 2003, 48(2): 286–289.CrossRefMathSciNetGoogle Scholar
W. Chen, Z. Guan, X. Lu. Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: An LMI approach[J]. Systems & Control Letters, 2005, 54(6): 547–555.zbMATHCrossRefMathSciNetGoogle Scholar
C. Lu, T. Su, J. Tsai. On robust stabilization of uncertain stochastic time-delay systems-an LMI-based approach[J]. Journal of the Franklin Institute, 2005, 342(1):473–487.zbMATHCrossRefMathSciNetGoogle Scholar
E. Fridman, U. Shaked. A descriptor system approach to H∞ control of time-delay systems[J]. IEEE Transactions on Automatic Control, 2002, 47(2): 253–279.CrossRefMathSciNetGoogle Scholar
Y. He, M. Wu, J. She, et al. Parameter-dependent Lyapunov functional for stability of time-delay systems with polytopic-type uncertainties[J]. IEEE Transactions on Automatic Control, 2004, 49(5): 828–832.CrossRefMathSciNetGoogle Scholar
Y. Wang, L. Xie, C. Souza. Robust control of a class of uncertain nonlinear system[J]. Systems & Control Letters, 1992, 19(1): 139–149CrossRefMathSciNetGoogle Scholar
Y. Li, X. Guan, D. Peng. Exponential stability criteria for uncertain stochastic systems[C]//Proceedings of the 27th Chinese Control Conference. Beijing: Beijing University of Aeronautics & Astronautics Press, 2008: 21–25.Google Scholar
E. Fridman, U. Shaked. Parameter dependent stability and stabilization uncertain time-delay systems[J]. IEEE Transactions on Automatic Control, 2003, 48(5): 861–866.CrossRefMathSciNetGoogle Scholar