The Stability Of Uncertain Switched System With Time-delay

Switched Systems, an important class of Hybrid Dynamic Systems, have extensivepractical background and great significance of theoretical study. It consists of a series ofsubsystems and switching sequence and a switching rule indicating the active subsystemat each instant of time. For switched systems, stabilization is not only an essentialrequirement, but also a focal point. While, time delay and uncertain are very commonphenomena in engineering systems. The existence of them will always lead to thesystem instability or function decline, so the study of the uncertain time-delay switchedsystem have intensity value and significance. In recent decades, more and more scholarshave pay attention to the study of the stability of switched systems. In order to get amore conservative result, scholars have put in a lot of efforts and gain a large number ofstability criterion which have a relatively small conservation. In these days, there appeara lot of new ideas and methods for the study of time-delay switched system. The resultof these methods has certain improvement on the basis of the original, but there is still alarge conservative.This paper studies the two classes of time-delay switched systems with uncertainly,and makes detailed analysis to the problem of the stability of the two types of system.Specific work is as follows:（1）First, the paper puts forward with a asymptotic stability criterion withtime-delay switched system. Systems model for generalized model change, Then,construct a suitable Lyapunov-krasovskii function and based on the Lyapunov stabilitycriterion, we give the sufficient conditions for the robust stability of the system.Because of the existence of time delay, in order to deal with time delay, we make thestability of a given criterion have less conservative with delay integral method.（2）Then, the paper gives the criterion of the stability of time-varying delayswitched systems. And the system has a norm to match the uncertainty. Systems modelfor generalized model change, then, construct a suitable Lyapunov-krasovskii functionand based on the Lyapunov stability criterion, we give the sufficient conditions for therobust stability of the system. Due to the introduction of liberty matrix, makes thesystem have a smaller conservatism.（3）It also studied the H control problem of switched systems with uncertainty.First, systems model for generalized model change, then, construct a suitableLyapunov-krasovskii function. We get a criterion with indicator. The last, summarize the full text and the direction of next step.