A Thesis Submitted To University Of Science And Technology Liaoning

Time delay is widely found in many practical systems, such as biological systems, social systems, economic systems, networked control systems, process control systems, etc. There are many reasons for delay appeared. The delay often leads to the deterioration of the performance of the control system even the stability of the system. Therefore, the stability analysis and synthesis problem of time delay systems are always the hot issues in the study of control theory. Based on Lyapunov stability theorem, the stability analysis of linear systems with time delay, uncertain time delay systems and neutral time delay systems are studied. The main contents are as followed:1. The basic knowledge of stability theory is introduced. Two important theorems Krasovskii stability and Razumikhin stability are introduced. At the same time, the method of linear matrix inequality(LMI) and related lemma are popularized. And the paper introduces the arrangement of the content. 2. The stability conditions for a class of linear time delay systems are obtained. First, the time delay interval is divided into two different intervals, and then by using the two integral inequalities and combining the free weight matrix the new stability criterion of time delay system is obtained. In this chapter, we deal with the derivative integral which is neglected in other literature, and which leads to less conservative. 3. Robust stability of a class of linear uncertain time delay is considered By using delay decomposition approach and integral inequalities, and the robust stability criterion is obtained are established in terms of linear matrix inequalities(LMIs). On the basis of the second chapter, because of the increase of the uncertain factors, it is more general and practical. Several numerical examples are given to show the superiority of the proposed methods. 4. The stability of a class of neutral delay systems is studied. The time delay interval is divided into two different intervals. Different from the related literature, using the reciprocal convex combination and the new integral inequality method, this method reduce the computation quantity and deal with the derivative integral which is neglected in other literature. 5. Finally, the conclusion and prospect of the paper is given.