A Class Of Stochastic Delay Systems, Robust Control,

The stochastic factors,time delays and uncertain parameters are frequently encountered in many practical systems.The existence of them makes the system analysis and synthesis become more complicated and difficult.Meanwhile,they are frequently the sources of instability and performance degradation in many dynamic systems.Uncertain stochastic systems with time delays have received much attention since such systems have come to play an important role in many branches of science and engineering applications.This dissertation investigates the problems of robust stabilization,robust H_∞control, robust guaranteed cost control and robust H_∞guaranteed cost control for a class of stochastic time-delay systems based on Lapunov-Krasovskii functional theory and linear matrix inequality(LMI) approach.The purpose of the robust stabilization problem is the design of a state feedback controller with distributed delays such that the closed-loop system is mean-square asymptotically stable for all admissible uncertainties.In the robust H_∞control problem,in addition to the mean-square asymptotic stability requirement,a prescribed H_∞performance is required to be achieved.In the robust guaranteed cost control problem,in addition to the mean-square asymptotic stability requirement,a given quadratic cost function has an upper bound.The purpose of the robust H_∞guaranteed cost control problem is the design of a memory state feedback controller with distributed delays such that the closed-loop system is mean-square asymptotically stable and satisfies a prescribed H_∞performance level and guarantees that a given quadratic cost function has an upper bound for all admissible uncertainties.In terms of a linear matrix inequality,delay-dependent sufficient conditions for the solvability of these problems are proposed respectively;the expressions of desired state feedback controllers are given.Via the MATLAB LMI Control Toolbox,numerical examples demonstrate the effectiveness of the present results.