Stability Analysis And Robust Controller Design For Stochastic Time-Delay Systems

In practical applications, many control systems inevitably encounter uncertainties and external disturbances. These uncertainties and external 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 included in many practical systems, such as networks control systems, production process control systems, population and economic dynamic systems and so on, the current and future states of the systems dependent on their past states. In recent years, the study of analysis and synthesis for stochastic time-delay systems, which are described by stochastic delayed differential equations, is a popular topic in the field of control theory.This thesis focuses on the problem of stability analysis and robust control for stochastic time-delay systems based on Lyapunov stability theory, Ito's formula, Schur lemma, stochastic analysis approach, and LMI approach. The main works of this thesis are as follows:1. With the idea of delay fractioning technique, the problem of stabiliy analysis for stochastic systems with time delays is investigated, including mean-square asymptotical stability or exponential stability in the mean square. We first consider the nominal systems of stochastic systems, and then the results are further extended to the stochastic time-delay systems with parameter uncertainties and nonlinearities. The parameter uncertainties are assumed to be time-varying norm-bounded appearing in both the state and input matrices. We propose a new approach to investigate the problem of stability analysis for stochastic time-delay systems. By using the stochastic analysis approach, inequality and free-weighing matrix technique, we introduce a novel Lyapunov-Krasovskii functional based on the idea of delay fractioning and establish delay-dependent stability criteria. Compared with the existing results, our developed method can greatly reduce the conservatism.2. We also investigate the problem of stabilization and robust H∞control for stochastic systems with time delays in the state. Based on the delay fractioning technique, a new approach is proposed to develop stabilization and H∞control for stochastic time-delay systems. Firstly, we consider the stabilization problem for stochastic time-delay systems. Secondly, we investigate the H∞control problem. We consider the nominal systems of stochastic systems, and then the results are further extended to the stochastic time-delay systems with parameter uncertainties. Suffcient delay-dependent conditions for the existence of state feedback controllers are proposed, which guarantee mean-square asymptotic stability and a prescribed H∞performance level of the resulting closed-loop systems. Moreover, the results are further extended to the time-delay systems without stochastic disturbances. The main idea is based on the delay fractioning technique, which differs greatly from most existing results and reduces conservatism.3. The problem of asymptotic stability for stochastic Hopfield neural networks with time delays is studied. New delay-dependent stability criteria are presented by constructing a novel Lyapunov-Krasovskii functional based on the delay fractioning technique.Finally, the concluding remarks are summarized, and the future research studies are pointed out.