H_∞, H₂/H_∞ And Guaranteed Cost Control For Stochastic Time-delay Systems

In this thesis, based on the Lyapunov stability theory, Ito formula, the principle of stochastic analysis, and the tools of Schur Complement, matrix inequalities, Lyapunov-Krasoviskill functional(function) etc. are employed to study stochastic time-delay systems, mainly for the problems of designing controllers of stochastic time-delay systems.The main contributions of the thesis are as follows:In the first, the H_∞control of a class of nonlinear stochastic time-delay system is discussed. The sufficient condition of the problem and the H_∞controller are obtained. Making use of the tool box of Matlab, we gain a numerical example.In the second, the H₂ /H_∞control of linear stochastic time-delay system is investigated. We obtain the sufficient condition of the problem, but find that the condition is nonlinear matrix inequalities difficult to be solved. We let P and Q take the special forms and give out the numerical example.In the third, the guaranteed cost control of uncertain stochastic time-delay system is considered. Firstly, we give out the conception of the guaranteed cost control, then using Theorem 1 presents the sufficient condition. Theorem 2 is the form of linear matrix inequality of the Theorem 1. Theorem 3 proves the optimality of the aim function under the condition of the guaranteed cost control law.