Robust stochastic stabilization and H control of uncertain stochastic interval time delay systems
This paper establishes a new robust delay dependent stabilization and H control methods for a class of uncertain stochastic time delay systems. The delays in state and control input are time varying continuous functions varying in an interval and uncertainties are norm bounded. An appropriate Lyapunov Krasovskii functional is constructed and a new technique to estimate the upper bound of the stochastic differential of Lyapunov Krasovskii functional is obtained. Based on the idea of delay decomposition and free weighting matrices, new and less conservative solutions to the stabilization and H control problem of uncertain stochastic time delay systems are provided in terms of linear matrix inequalities. A robust state feedback controller is proposed to guarantee mean square asymptotic stability as well as the prescribed H performance for the closed loop systems. The advantages of the results proposed in this paper, which differ greatly from most of the existing results, lie in their reduced conservatism by thinning the delay partitioning. Numerical examples are provided to show the advantages of the proposed technique.
IMA J. Math. Control. Inf.