| Time-delay is a widespread physical phenomenon accompany with the transmission process of substance and energy. There exist many practical systems, for example economy systems, zoology systems, power systems and networked systems, are all time-delay system. On the other hand, the study shows that time delays are regarded as one of the main sources causing instability and degrading performance of control systems. To ensure the stability and good dynamic performance of time-delay systems, appropriate controller design approach should be provided. In addition, some states are difficult to be measured directly. Therefore, for stabilization purpose, it is necessary to estimate the state. Thus, to investigate the filter, observer and controller design method of time-delay system is of importance in theory and application.This dissertation focuses on the filtering for stochastic time-delay system with nonlinear disturbance, the filtering and the observer-based state feedback control for interconnected time-delay system, by virtue of Lyapunov-Krasovskii functional and convex optimation technology, reciprocally convex approach and Jensen inequalities. The main research works are listed as follows:1. For the stochastic system with discrete and distributed time delays, by Lyapunov-Krasovskii approach based on the delay partitioning and integral partitioning technique, we first develop a less conservatism sufficient condition guarantees the system to be mean-square exponential stable. Based on the obtained result, by virtue of singular value decomposition approach, the L2–L∞ filtering problems for stochastic systems with delayed nonlinear perturbations are solved.2. For a class of stochastic systems with Markovian jump parameters, external disturbances, It?-type Brownian motions, and mixed mode-dependent time-varying delays, the mean-square exponential stability and L2-L∞filtering are investigated. Due to the system modes and time-delay modes are asynchronous, and the mixed time delays are mode-dependent, a delay-range-dependent, mixed mode-dependent and decay-rate-dependent Lyapunov-Krasovskii functional is chosen to decrease the conservatism. By virtue of reciprocally convex approach and Jensen integral inequality, the exponential stability criterion is established for the filtering error system, and a new L2-L∞ filter design method is developed in terms of linear matrix inequalities(LMIs).3. The concept of finite-time stability and finite-time bounded are extented to interconnected Markovian jump system with mode-dependent time delays. By constructing delay-range-dependent, mode-dependent and parameter-dependent Lyapunov-Krasovskii functional, combined with reciprocally convex approach and Jensen integral inequality, the conditions of finite-time bounded are proposed. And the decentralized finite-time H? filter design method is developed in terms of linear matrix inequalities(LMIs).4. For the interconnected Markovian jump system with mode-dependent time delays, by constructing delay-range-dependent, mode-dependent and decay-rate-dependent Lyapunov-Krasovskii functional, using reciprocally convex approach and Jensen integral inequality, using Lyapunov-krasovskii stability theory and LMI approach to establish the mean-square exponential stability condition. And H∞ state feedback control utilizing global state informations and state feedback control utilizing global state informations of decentralized observer are also developed. Finally, Numerical simulation of a power system, composed of three coupled machines, is used to illustrate the effectiveness of the obtained results.5. For nonlinear interconnected time-delay system, by virtue of Lyapunov-Krasovskii functional and Jensen integral inequality, the time-delay-dependent and decay-rate-dependent exponential stability condition is established firstly. Moreover, a new observer-based H∞ decentralised controller design method is developed. Finally, the obtained result is used to control a 3-machine-9-bus power system to illustrate its effectiveness.
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