Some Research On The Stability Of The Linear Singular System

Exponential stability and finite time stability are new concepts, which are quite different from the classical stability. They are recently attracting considerable interests. According to the actual background, many complex problems can be described as finite time stablity problem. The recent decades have witnessed the great development of researches on the study of finite time stability, which plays a significant role in designing the satellite orbit and chemical engineering. In this paper, with the help of linear matrix inequality and using Lyapunov functions, we discuss the finite time stablity problem on different systems.In chapter one, firstly, we state the background, the existing results, and the major contributions of exponential stability and finite time stability. Then, the definitions of exponential stability and finite time stability are stated.In chapter two, we study the stability problems and L2-gain analysis for switched singular linear systems with jumps. Based on the concept of average impulsive interval, some novel sufficient conditions on the stability and L2-gain for switched singular linear systems with jumps are developed. Two examples are given to illustrate the effective-ness of the results. Two numerical examples are given to illustrate the effectiveness of the results.In chapter three, we study the robust finite-time stability for singular systems with parameter uncertainty and impulsive jumps. Based on the concept of average impulsive interval, some novel sufficient conditions on the finite-time stability are developed. It is shown that the obtained results are less conservative than some existing criteria. One example is given to illustrate the results.