H_∞ Control And Filtering For Markovian Jump Systems With Time Delay

It is quite common for a practical system having a variable structure due to interconnection failures and repair, or environment disturbances, etc. Markovian jump models are often introduced in order to describe this character. The systems combine time-driven factors with event-driven factors, and jump stochastically among the different modes. According to the practical background of Markovian jump systems, much attention has been drawn from the literature. Meanwhile, time delay is inevitable in real systems, which will affect the performance of the systems. So how to overcome the affect of time delay is not only theoretical but also of practical importance. Recently, analysis and synthesis for time delay systems, especially Markovian jump systems with time delays have appealed a lot of researchers in the control theory community.This dissertation concerns with the problem of stability analysis and control for Markovian jump systems with time delays, constructs some effective criteria and obtains a serial of significant results according to Lyapunov stability theory, Linear Matrix inequality, weak infinitesimal operator, Grownwall-Bellman lemma, Dynkin formula, Shur complement lemma, and Jensen’s inequality. This dissertation goes from the easy to the di?cult and complicated, first treats with Markovian jump systems with constant time delay, then a more general and complex case, Markovian jump systems with mode dependent time-varying delays. The main research work of this dissertation is as follows:First, we studies the problem of stochastic stabilization for a class of Markovion jump systems with time delay. A new delay-dependent stochastic stability criterion on the stochastic stability of the system is derived based on a novel Lyapunov-krasovskii functional approach. The equivalence and superiority to existing results are demonstrated.Then we is concerned with the problem of H∞ performance analysis. The proof of equivalence with some former results under some specific case is presented, and the advantages of proposed results are also shown.Second, based on the stability criterion of Markov jump systems with time delay,the state feedback controllers are designed, which guarantee the stochastic stability of the closed-loop system. By constructing a new Lyapunov-Krasovskii functional, a more effective criterion for H∞ performance analysis is obtained. Based on it, the procedure to design H∞ state feedback controllers is provided, which guarantees the stochastic stability and a prescribed H∞ performance for the closed-loop Markovian jump systems with time delays.Third, based on H∞ performance analysis, we consider the robust H∞ filter design for uncertain Markovian jump linear systems with time-varying delays. The purpose is to improve the existing results on these problems. a new delay-dependent bounded real lemma is derived. It is shown that the presented stability criterion and the BRL are less conservative than the existing ones in the literature. Then with the new BRL, delaydependent conditions for the solvability of the addressed H∞ filtering problem are given.the problem of exponential estimates is studied for Markovian jump systems with timevarying delays. Based on the idea of delay partitioning, a new Lyapunov-Krasovskii functional is constructed and the exponential stability criterion is proposed, which could be used for estimates of exponential decay rate λ. Meanwhile the method to compute exponential decay coe?cient σis also presented.