Robust Stability And Control Synthesis For Time-Delays Systems With Uncertainty

In a number of industrial processes, there are time delays in a large amount of physical systems, such as Chemical Systems, Lossless Transmitting Systems, Turbojet Aircraft, Nuclear Reactor and Network Control Systems which are very popular now. Because of the existence of time-delays which will change the proper equations of these systems, time delay is one of the main factors to lead to instability of these systems and performance deterioration of the controlled systems. As a result, the research on stability of the time delay systems attracts considerable attention in the control theory literature all along. On the other hand, in engineering practice, it is very difficult for the researchers to obtain the exact mathematical model of the controlled systems by influence of external environment and interior technique. Adoptive model for design process of control systems is generally mathematical model, which is handled in the method of linear approximation to a certain extent, so the model under which the controller is designed is usually different from the real plant. In a sense speaking, the differences can be usually described as the uncertainties in the model arguments and the uncertainties are measurable and can be restricted in some range, such as parameter uncertainties which is bounded or convex polynomial. Then, Robust Control Theory is an effective way to deal with the uncertainties of the control systems.Base on Lyapunov Stability Theory and Linear Matrix Inequality Method, some free weighting matrices which represent the relation of each term in these described systems are introduced. On account of a class of uncertain time-varying time-delays systems with norm- bounded parameter uncertainties, state-delays and control input-delays, the problem of robust stability criteria and the design of methods of robust stabilizing controller by three feedback controllers, such as memoryless state feedback controller, static output feedback controller and dynamic output feedback controller,are investigated, the delay-dependent stability criteria is obtained.There are five chapters in this paper:In chapter 1, the background of the paper is introduced, including the research status of the uncertain time-delay systems, the general situation of Robust Control Theory and robust research of time-delay systems. Finally the main work, purpose and significance of this paper are introduced.Chapter 2 introduces this knowledge of preparation, the required basic knowledge, and a number of basic theorems of the paper. Finally these relevant lemmas of the paper are introduced.In chapter 3, for a class of linear time-varying delay systems with state delays and control input delays, asymptotic stability problem is considered. At the same time, delay-dependent stability criterion of the system and the design methods of several feedback controllers are presented. Finally, some simulation results are also given.Based on the system which is discussed in the previous chapter, we add some uncertainties to it. The chapter 4 discusses the robust stabilization problem about a class of uncertain time-varying delay systems with state delays and control input delays, at the same time, the sufficient conditions of the delay-dependent Robust stabilization and the design methods of three feedback controllers are presented. Two numerical examples are given for checking correctness and effectiveness of the results.In chapter 5, the results on this research in the paper are summarized and prospected.