Discrete bilinear stochastic systems with time-varying delay: Stability analysis and control synthesis

This paper deals with the problems of stability analysis and static output-feedback stabilization for discrete stochastic 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 software. 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 minimization 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.