Abstract
The p-moment exponential robust stability for stochastic systems with distributed delays and interval parameters is studied. By constructing the Lyapunov-Krasovskii functional and employing the decomposition technique of interval matrix and Itô’s formula, the delay-dependent criteria for the p-moment exponential robust stability are obtained. Numerical examples show the validity and practicality of the presented criteria.
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Eurich, C. W., Thiel, A., and Fahse, L. Distributed delays stabilize ecological feedback systems. Physical Review Letters 94(15), 158104(4) (2005)
Wang, Z., Liu, Y., Fraser, K., and Liu, X. Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays. Physics Letters A 354(4), 288–297 (2006)
Su, W. W. and Chen, Y. M. Global robust stability criteria of stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays. Communications in Nonlinear Science and Numerical Simulation 14(2), 520–528 (2009) DOI: 10.1016/j.cnsns.2007.09.001
Florchinger, P. Stability of some linear stochastic systems with delays. Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, Florida, USA, Dec. 2001, 4744–4745 (2001)
Verriest, E. I. Stochastic stability of a class of distributed delay systems. Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005, Seville, Spain, 5048–5053 (2005)
Ficak, B. Point delay methods applied to the investigation of stability for a class of distributed delay systems. Systems & Control Letters 56(3), 223–229 (2007)
Mao, X., Koroleva, N., and Rodkina, A. Robust stability of uncertain stochastic differential delay equations. Systems & Control Letters 35(5), 325–336 (1998)
Liao, X. X. and Mao, X. Exponential stability of stochastic delay interval systems. Systems & Control Letters 40(2), 171–181 (2000)
Lu, C. Y., Su, T. J., and Tsai, J. S. H. On robust stabilization of uncertain stochastic time-delay systems-an LMI-based approach. Journal of The Franklin Institute 342(5), 473–487 (2005)
Chen, W. H., Guan, Z. H., and Lu, X. M. Delay-dependent exponential stability of uncertain stochastic systems with multiple delays: an LMI approach. Systems & Control Letters 54(6), 547–555 (2005)
Jiang, M. H., Shen, Y., and Liao, X. X. Robust stability of uncertain neutral linear stochastic differential delay systems. Appl. Math. Mech. -Engl. Ed. 28(6), 741–748 (2007) DOI: 10.1007/s10483-007-0613-x
Mao, X. Exponential Stability of Stochastic Differential Delay Equations, Marcel Dekker, New York (1994)
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Communicated by Li-qun CHEN
Project supported by the National Natural Science Foundation of China (No. 70473037) and the Natural Science Foundation of Henan Province of China (No. 0611054400)
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Su, Ch., Liu, Sf. The p-moment exponential robust stability for stochastic systems with distributed delays and interval parameters. Appl. Math. Mech.-Engl. Ed. 30, 915–924 (2009). https://doi.org/10.1007/s10483-009-0710-x
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DOI: https://doi.org/10.1007/s10483-009-0710-x