Stability And Sliding Mode Control For Time-Delay And Stochastic Systems

In the modern control field, the sliding mode variable structure control (SMVSC) was adopted in the control systems, which has many advantages, such as the simple control algorithm to be easy to realize and sliding mode is invariant to internal and external interference. A system only consider the designing sliding mode control itself is not enough, must according to the different specific systems, leaning from new progress and new discoveries of other control theory to further expand and develop the sliding mode control theory for uncertain system with time-delay; switched system is a class of hybrid systems of a influential important type, due to the switched system has extensive actual background and simple structure, at the same time, the research methods and results of the switched system which often provide the theoretical and methodological reference and inspiration for the study of a general hybrid system. Therefore, the study of the stability and control theory for the switched systems has a very important academic value and significant applications.The main contents of the paper are as follows:1. The overview for the development and study of the sliding mode control theory and the overview for the switched system are summarized.2. In this paper, the problem of designing a variable structure control is investigated for uncertain polytopic systems with time-delay. Firstly, by employing linear matrix inequality (LMI) method, a sufficient condition is derived for the existence of linear sliding model. Secondly, the variable structure control law is designed, which not only guarantees the system to reach the sliding model in finite time, but also assures it to be robust quadratic stable on the sliding surface. Finally, a numerical example illustrates the feasibility and effectiveness of the proposed method. 3. The robust H-infinity sliding-mode control is addressed for a class of stochastic switched systems with mismatched uncetainties and external disturbances. Based on the linear matrix inequality (LMI) technique and the single Lyapunov function approach, a single H-infinity sliding surface and a switching law are designed such that the sliding mode dynamic equation of stochastic switched systems is robustly asymptotical stability; Furthermore, a concept of the subordinated reachability of the sliding surface is introduced, the sliding mode controller is designed to ensure that the sliding surface is subordinated reachable. A numerical example illustrates the effectiveness of the proposed design method.4. The problem of delay-dependent asymptotic stability of the equilibrium point is studied for the switched Hopfield neural networks with time-delay under uncertainty, An dwell time method is introduced into switched Hopfield neural networks in this article. Then we utilizing the Lyapunov functional method and combining with the linear matrix approach. Based on the dwell time method, a sufficient condition ensuring the delay-dependent asymptotic stability for the switched Hopfield neural networks is obtained. An illustrative example is given to demonstrate the effectiveness of the proposed method.