Discrete bilinear stochastic systems with time-varying delay Stability analysis and control synthesis精品.pdfVIP

Chaos, Solitons and Fractals 34 (2007) 394–404 /locate/chaos Discrete bilinear stochastic systems with time-varying delay: Stability analysis and control synthesis Huijun Gao a,*, James Lam b, Zidong Wang c a Space Control and Inertial Technology Research Center, Harbin Institute of Technology, P.O. Box 3015, Yikuang Street 2#, Nangang District, Harbin 150001, China b Department of Mechanical Engineering, The University of Hong Kong, Hong Kong c Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom Accepted 9 March 2006 Abstract This paper deals with the problems of stability analysis and static output-feedback stabilization for discrete stochas- tic systems with time-varying state delay. A delay-dependent condition for mean-square asymptotic stability is first established in terms of linear matrix inequalities (LMIs), which can be solved efficiently via available numerical soft- ware. Connection with an existing result on related topics is thoroughly discussed. Based on the established stability criterion, the problem of static output-feedback stabilization is then investigated, which is cast into a nonlinear mini- mization problem involving LMI constraints. An iterative algorithm making use of sequential linear programming matrix method (SLPMM) is proposed to solve the nonlinear minimization problem. A numerical example is provided to demonstrate the feasibility and applicability of the proposed approaches. 2006 Elsevier Ltd. All rights reserved. 1. Introduction During the past few decades, stochastic modeli