Stability Of Uncertain Stochastic Systems With Time Delays

In this dissertation, based on the Lyapunov stability theory, It? 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. In this dissertation, there are the stability of linear stochastic systems with time-delays, stochastic Lurie systems with time-delays and Lurie systems with time-delays and systems with distributed delay.The main contributions of this dissertation are as follows:In the first, using It? formula and Lyapunov functions, we establish sufficient condition of robust stability of uncertain stochastic systems with time-delays and exponential stability of uncertain stochastic systems with time-varying delays. The independent sufficient condition is derived in terms of linear matrix inequality (LMI). By the conclusions, we obtain a corollary.In the second, this dissertation deals with the problem of robust absolute stability for Lurie control system with time-delays. Using Lyapunov function, we establish sufficient conditions of robust absolute stability for stochastic interval Lurie direct control system with time-delays and stochastic interval Lurie indirect control system with time-delays. The criteria are expressed by Linear matrix inequality (LMI).In the third, exponential stability in mean square of the uncertain distributed delay stochastic system is considered. Lyapunov-Krasovskii functional, It? formula and linear matrix inequality approaches are employed.