Robust Control For Delay Stochastic Systems

In practical applications, many control systems inevitably encounter uncertainties and external disturbances. These uncertainties and disturbances usually impact systems in a stochastic way. Considering this, it is necessary to adopt a stochastic model to describe an engineering dynamic system. On the other hand, time delays are frequently found in many control systems; the existence of time delays is usually one of the main causes of instability and worse performance for a system. Therefore, investigating the stability and the control of delay stochastic systems is very important in theoretical and engineering sense.This paper considers uncertain stochastic systems with delays in states and inputs; we mainly focus on the problems of state feedback robust control in the following aspects: The robust stabilization; robust H_∞ control; guaranteed cost control; H_∞ guaranteed cost control; non-fragile stabilization; non-fragile H_∞ control; and non-fragile guaranteed cost control. With applications of the theories and approaches of Lyapunov stability, quadratic stabilization of time-varying uncertain systems, Ito formula, Schur complement lemma, linear matrix inequality (LMI), we transform the control problems into a feasible issue of certain LMIs. Some sufficient conditions for the solvability of the problems are obtained. The expressions of the desired controller are given. "Via the MATLAB LMI control toolbox, we provide simulation examples to illustrate the application and effectiveness of the proposed methods.