Stability And Finite-time H_∞ Control Of Large Delay Systems

As an important index to measure the system performance,stability has always been a key issue that many scholars pay attention to,including the asymptotic stability defined in an infinite time interval,the finite-time stability and finite-time boundedness defined in a finite time interval.In general,stability of the system is a prerequisite for ensuring its normal operation.However,due to the ubiquity of the delay,the performance of the system could deteriorate,and it can even make the system unstable or out of control.Therefore,the stability and control synthesis for delay systems have become a hot topic for the control community.It was assumed that the delay is small in past works.That is to say,the upper bound of the delay is a small value.But in real systems,the delay may exceed the derived upper bound in a moment,and the stability of the system remains unchanged.Thus,the obtained results will be more conservative.And it is very necessary to study the system performance under the influence of the large delay.In this paper,the stability conditions and the finite-time H∞ control problem for linear systems with large delay are investigated by using the switching method and Lyapunov functional method.This paper involves the following aspects:stability and L1-gain performance analysis for linear large delay positive systems,robust finite-time H∞control for linear uncertain large delay systems.The main work of this paper is as follows:In the second chapter,the stability and L1-gain performance analysis for the linear positive systems with large delay are discussed.First,the original system is transformed into a positive switched delay system with two subsystems by exploiting the switching method.One of the subsystems is stable,while the other is unstable.Second,considering the influence of the large delay,a special Lyapunov functional with large delay integral terms is chosen.Then,under the constraint of frequen-cy and length rate of large delay period,the sufficient conditions are obtained to guarantee that the linear large delay positive systems are exponentially stable with L1-gain performance.And a numerical example is given to illustrate the validity of the proposed method.In the third chapter,the robust finite-time H∞ control problem for linear un-certain large delay systems is studied.First,the switching method is employed to separate the original system into two situations:small delay and large delay.Second,by using the Lyapunov functional method,a state feedback controller is designed to guarantee that the closed-loop system is finite-time bounded within the limitation of the frequency and length rate of large delay period.Then,the finite-time H∞performance of the closed-loop system is analyzed.Finally,the effectiveness of the conclusions is demonstrated by a numerical example.Finally,we summarize the full text and propose further research goals.