Robust H_∞ Performance Of A Class Of Uncertain Boundary Uncertain Sampling System

With the development of science and technology, people have entered the digital age.Networked control system also has advanced by leaps and bounds. In recent years, with the rapid development of the impulsive technology, digital component parts, digital electronic computer,in particular, the rapid development of the new technology such as the microprocessor, digital controller has replaced analog controller on many occasions. Sampling controller design is a key problem of sampled-data control theory, which provides theoretical guidance for the computer control. The key problem is to study the stability of the sampled-date control system. As is known to all that the actual system is usually most complicated, it may appear a variety of the combination of complex characteristics which consists of uncertainty, infinite dimension,nonlinearity, and so on. The coexistence of continuous signal and discrete signal is not only the outstanding characteristics of sampled-data control system, but also a difficulty of sampled-data system analysis and design as well. At present, the design methods of sampling controller mostly aim at discrete-time and impulsive system method. Based on an input delay approach, the stability of the sample data control and the sampled data control problem of uncertain system were studied.Based on an input delay approach, sampled-data control system was transformed into a continuous time-delay system. With the theory of sample-data control and Lyapunov stability theory, a zero-value term was introduced. Sufficient conditions for exponential stability of uncertain system, with which linear sampling is presented in terms of linear matrix inequality(LMI). Simulation example was given to demonstrate the effectiveness and correctness of the proposed method. This thesis is divided into five chapters:In chapter 1, we introduce the background of the research for delay systems, and make a detailed review. On this basis, we indicate the main issues in this paper.In chapter 2, we briefly introduce the theoretical knowledge of stability, like Lyapunov stability criterion and several important lemmas, which make full preparation for the follow-up work.In chapter 3, by using Lyapunov method and the lemma of the second chapter and combing convex optimization method, we give a sufficient condition for stability of sampled-data control system and H?performance. In the end of the chapter, we obtain the numerical simulation results in LMI tool case of MATLAB and testify the feasibility of stability criterion. We show the result that we obtained through the theoretical analysis and numerical example, which is better than some results have obtained at present already in conservatism and complexity.In chapter 4, this chapter’s problem is based on chapter 3. It was studied the stability of uncertain system. Based on Lyapunov method, the criteria of sampled-data control system with parameter uncertainties was studied. Finally, we obtain the numerical simulation results in LMI tool.In chapter 5, we summarize the entire thesis, and point out the future researching direction.