Robust H_∞ Control For Discrete Time-Delay Systems

Since mathematical models are abstracted from the practical problems, many of which are given in the form of discrete systems, for instance, social systems of population distribution problems, cobweb model in market economy, discrete systems and people's daily life are also closely related, for example, nutrition department can establish a mathematical model in the form of discrete system according to the relationship between energy intake, metabolism, sports and weight to scientifically formulate weight-loss plan. With the wide range applications of computer in system analysis and control, time discretization has become more and more important, for example, we use digital computer to analyze the continuous-time systems, or use discrete control devices to control continuous-time control systems, we will encounter the problem of the continuous-time system transformed into an equivalent discrete time system. In the industrial production process, system uncertainty and time delay is often inevitable and also can not be ignored, uncertainty and time delay are also the main factor affecting the system stability. Therefore, the study of robust control for uncertain discrete time-delay systems also have practical significance to some extent.Based on Lyapunov stability theory, and H∞control theory, combined the properties of linear matrix inequality, the problem of robust H control for discrete time-delay systems are discussed. The main contents are as follows:Chapter 1:The required theorem and temma are summarized.Chapter 2:The robust stability problem for a class of discreat time system with state and input delays was discussed. Applied Lyapunov method, and combined the properties of matrix inequality, a sufficient condition was provided for designing a state feedback Controller. The condition is delay-independent. The results obtained were depended on the solution of a corresponding LMI respectively. An example ellustrated the validity of the criteria obtainedChapter 3:The problem of H∞feed back control for discrete-time delay system with state and input delays, delay-dependent robust dynamic output feeddbc H∞control for uncertain discrete time-delay system, delay-dependent robust H∞filtering for uncertain discrete time-delay system are discussed...