Delay Stochastic System Stability And Robust Control

In practical applications, there inevitably exist parameter uncertainties, stochastic disturbances, time-delays, and exogenous disturbances with bounded energy.As the performance requirements of the systems are becoming more and more higher, all these factors should be taken into consideration when analysing the system performances. Hence, it is of great importances to study the stability and robust control problem for uncertain stochastic systems with time-delays.The uncertain stochastic system with time-varying delays in states and inputs is considered in this paper. Lyapunov stability theory, Ito differential formula, Schur complement lemma, LMI approach, descriptor system approach and Lyapunov-Krasovsldi function are employed to study the mean square exponential stability of the system and the robust stabilization, the robust H_∞control, the guaranteed cost control, the H_∞guaranteed cost control problem of the system.First delay-free and delay-dependent conditions for stability of the system of concern are obtained. Then based on the stability result, The controllers are designed respectively to stabilize the system and satisfied corresponding H_∞performance and guaranteed cost performance.The sufficient conditions proposed in the paper can be solved via LMI. Examples are provided to illustrate the effectiveness of the proposed methods.