A Class Of Linear Continuous Time And Discrete Time Systems Limited Time H_ Up Control Problem Research

In the theoretical research of robust control, the researchers are concerned that the stability of the system is Lyapunov stability. Lyapunov stability is a portrait of the performance of the system on infinite interval, it does not reflect the system’s transient performance. The system which is stable in the sense of Lyapunov may have a bad transient performance, sometimes it is even impossible in engineering application. Therefore in practical engineering, people are often concerned that the system should satisfy certain transient performance requirements. The stability of the finite-time just can solve this problem, so in recent years the limited-time control of the control theory become one of hot issues.This paper studies a class of continuous time and discrete-time systems with limited time H∞control. First, with the definition of the finite-time stability and H∞performance control, leading to "limited-time H∞control", then by constructing the Lyapunov function method using formula we give the relevant theorem of a class of continuous-time linear systems with limited-time H∞control. Finally a simple example illustrates the feasibility of the theorem. Next, the study of discrete system, firstly with the help of a lemma we give the system a sufficient condition of finite time bounded, then using a similar approach we give the discrete-time linear system with limited-time H∞control a sufficient control. Finally, the feasibility and effectiveness of the system of finite time bounded sufficient conditions is verified.