Analysis and Synthesis of Stochastic Time-Delay Systems
|Course||Control Science and Engineering|
|Keywords||It(o ^) Stochastic Systems integral inequality delay-dependent control and filtering passive observer Markovian jumping systems neural networks|
The nondeterministic （i.e. stochastic） phenomena are frequently encountered in many practical systems. These systems should be described by stochastic differential equations instead of ordinary differential ones. 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, i.e. the current and future states of the systems dependent on their departed states. In recent years, the study of analysis and synthesis of 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 analysis and synthesis of stochastic time-delay systems based on Lyapunov-Krasovskii theory and LMI approach. The main works of this thesis are as follows:1. Based on an integral inequality, the exponential stability of deterministic time-delay systems is investigated. It is proved that the obtained result is equivalent to certain existing one. But our result is simpler, since it has less dimensions of LMI and less number of variables. By analyzing the main results of systems with time delays, the integral inequality method is proposed to investigates stochastic delayed systems. By introducing an additional vector, an integral inequality in stochastic context is derived. Based on this inequality and free-weighting matrix technique, delay-dependent method for stochastic delayed systems is established. This new method is employed to discuss exponential mean-square stability of stochastic systems with delays, which avoids model transformations and bounding techniques for cross terms. While dealing with the nonlinear perturbation which satisfies Lipchitz linear growth condition, the matrix inequality condition in existing reports is removed by using the trace characteristic of vector and matrix, such that the result is less conservative.2. Based on integral inequality approach, the problems of delay-dependent ro- bust stabilization, robust H∞control and observer-based output feedback control for stochastic delay systems are considered. If there is no stochastic perturbation, the bounded real lemma （BRL） is equivalent to some existing ones in deterministic setting but with simpler forms. Based on singular value decomposition （SVD） approach, the condition for the existence of observer-based output feedback controller is formulated in terms of strict LMIs.3. The stochastic passivity of stochastic time-delay systems is investigated by using integral inequality method. The stochastic passivity of stochastic systems is defined by extending the deterministic ones. Delay-dependent passivity condition and control for stochastic delayed systems are presented.4. The issues of delay-dependent L2- L∞and H∞filtering for stochastic time-delay systems are handled by applying the integral inequality method. The presented L2-L∞performance result is equivalent to some existing one, which is obtained by using free-weighting matrix technique, but our result is simpler.5. By integral inequality approach, delay-dependent stability and H∞performance analysis for stochastic delayed systems with Markovian jumping parameters are discussed. In addition, delay-dependent stability and state estimation for stochastic delayed neural networks are considered.Finally, the concluding remarks are summarized, and the future research studies are pointed out.