The Input Output Finite Time Stability Analysis Of Singular Systems

With the development of science and technology and the needs of the large engi-neering technology, singular system which was more general than the normal systems was put forward in the 1970 s, which appeared in the electric power, aerospace, econ-omy, biology and many other practical system model. From the current research trends, hybrid singular system has absorbed more and more attention. So far, the results focus on Lyapunov asymptotical stability and exponential stability, which is a dynamic property defined in infinite time interval. In practical application, how-ever, we usually pay attention to the transient behavior of the system in a finite time interval. Thus, the investigation of finite time control problem of hybrid singular systems has far-reaching significance. This dissertation surveys the recent results on hybrid singular systems and gives a in depth study on the finite time control theory. The main content of the thesis and the research results are as follows:This paper discussed the input output finite time stabilization problem for time varying singular systems. The output and the input refer to the controlled output and the disturbance input, respectively. Two classes of disturbance inputs are con-sidered, which belong to L2 and L∞. Firstly, sufficient conditions are provided which guarantee the input output finite time stability for singular systems. Secondly, suffi-cient conditions are provided which guarantee the input output finite time stability for singular systems with uncertainties.Based on this, input-output-finite-time stabilization of continuous switched sin-gular systems with time-varying delay and its closed-loop systems is studied fur-ther. Firstly, we introduce the concept of input-output-finite-time stability and related lemmas; Secondly, by using mode-dependent average dwell time method and Lyapunov function method, we provide sufficient conditions to guarantee that the switched singular system with time-varying delay is regular, impulse free, and input-output-finite-time stable. Then, we design the state feedback controller to ensure that the closed-loop systems is input-output-finite-time stable.