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Delay-dependent exponential stability criteria for stochastic systems with polytopic-type uncertainties
Received:February 14,2008  Revised:July 24,2008
Keywords:Stochastic system  Exponential stability in mean square  Time-varying state delay  Delay-dependent criteria  Linear matrix inequality (LMI)
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Yumei LI, Xinping GUAN, Dan PENG , Changchun HUA, Xiaoyuan LUO Institute of Mathematics and System Science, Xinjiang University, Urumuqi Xinjiang 830046, China; Institute of Electrical Engineering, Yanshan University, Qinhuangdao Hebei 066004, China 
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Abstract:
      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.
Yumei LI, Xinping GUAN, Dan PENG , Changchun HUA, Xiaoyuan LUO.Delay-dependent exponential stability criteria for stochastic systems with polytopic-type uncertainties[J].Journal of Control Theory and Applications,2009,7(3):291~296.
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