Robust Stability, Stabilization And Control Of Time-delay Stochastic Systems

In this dissertation, based on the Lyapunov stability theory, Ito formula, the principle of stochastic analysis, and the tools of Grownwall-Bellman inequality, Schur Complement, matrix inequalities, Lyapunov-Krasovskii functional (function) etc. are employed to study stochastic delay systems. Mainly, the systems with comprehensive type of distributed delay are concerned about, the problems of robust stability and the design of robust controllers are considered. Especially, stability and stabilization of distributed delay systems with Markovian jumping parameters is deeply studied. Some efficiency criteria are established. Significant results are obtained.The main contributions of this dissertation are as follows:In the first, Exponential stability of a class of stochastic control systems with uncertain parameters is discussed. The fact that the optimal controller of nominal system can guarantee the robust stabilization of the systems is shown. The robustness of the optimal controller for uncertain parameters of systems and the algebraic criteria of exponential stability in mean square are obtained.Second, robust stability of systems with Markovian jumping parameters and with uncertainties is considered. The stochastic algebraic Riccati equation and corresponding optimal controller are employed. Based on the above factors, the robustness of the optimal regulator is analyzed. The robust performance of the optimal controller of nominal system about the disturbance of Markovian jump parameters and structural uncertainties is obtained. The un-definiteness of weight matrix is maintained. Numerical example is illustrated to show the correctness of the results.In the third, a class of stochastic differential systems with Markovian jumping parameters and white noise as well as distributed delay is studied. The robust stabilization of the optimal controller that is derived by stochastic linear quadratic optimal control problem about the uncertainties and the jumping parameters is considered mostly. Exponential stability in mean square of the systems is analyzed. The delay independent and delay dependent algebraic criteria are established. The robustness of optimal controller for the disturbance of the delay and Markovian jumping parameters is shown. The delay dependent, less conservative, sufficient condition is obtained.Fourth, the traditional linear quadratic (LQ) optimal control problem has been...