Filtering And Control Problems Of Discrete Systems With Delays And Uncertain Parameters

One of the main purposes of control systems is their ability to maintain acceptable behavior and meet certain performance reqiuirements even in the presence of sudden changes in the system dynamics.In many practical applications,abrupt changes of the systems can cause great difficulties in measuring the state of the systems.These changes can be due,for instance,sudden environment disturbances,random failures and noise,etc.Therefore,as two distinct classes of stochastic systems,it is necessary to apply filtering and control techniques to the system with Markovian jumping and stochastic system subjected to noise.In this paper,the filtering and control problems of discrete-time systems are investigated and two issues are discussed:the problem of robust H? filtering for discrete-time Markovian jump systems with time-varying delay and norm-bounded parametric uncertainties,two is the linear quadratic optimal control for discrete-time systems with delay and parametric uncertainties.In Chapter 3,the problem of robust filtering for discrete-time Markovian jump sys-tems with time-varying delay and norm-bounded parametric uncertainties is studied.A filter is designed in the presence of time-varying delay and parameter uncertainties.The filtering error system is proved to be stochastic bounded and satisfy correlative H? performance.Sufficient criteria are derived via constructing a novel delay-dependent Lyapunov-Krasonskii functional with convex hull and solving linear matrix inequalities(LMI),which guarantee the filtering error system to be stochastic finite-time boundedness in H? sense.Finally,an example is presented to illustrate the validity and feasibility of the proposed methods.In Chapter 4,the linear quadratic optimal control problem for discrete-time systems with delay and parametric uncertainties is explored.Based on the principle of dynamic programming,the optimal controller is designed by analyzing the system and calculating the mathematical expectation.Finally,an example is given to expound the validity of the conclusion.