Stability Analysis Of A Class Of Interval Time-varying Delays Systems

Time-delay phenomena is widely found in a variety of practical systems,such as sewage treatment systems,radio communication system,and so on.Time-delay may cause deterioration or instability of system,reduce system performance or cause chaotic phenomena in the system.Therefore,the research on stability analysis and synthesis of time-delay systems has been a hot topic among many scholars.This paper is mainly based on the stability theory,focusing on the stability problem of a class of linear switched systems with interval time-varying delays.We construct a Lyapunov-Krasovskii functional(L-K functionl)with a quadruple integral form.By using the methods of third-order inverse convex combination and multiple Wirtinger integral inequality method,we make the integral terms of L-K functional along the time derivative have smaller boundary values.Thus,in theory,a stability conservative criterion with less conservativeness is obtained.The main content and the corresponding results obtained through this study contain the following aspects:1.The basic knowledge of the stability theory of time-delay systems is introduced;the two methods for studying the stability analysis of time-delay systems are introduced:that is"frequency domain method"and"time domain method",also,the advantages and disadvantages of the research methods related to"time domain method"are emphatically analyzed;besides,the content of the full text are made and reasonable arrangement.2.The stability analysis of interval time-varying delays systems is discussed,through which a new stability criterion is established by constructing a class of L-K functional with upper and lower bounds of time-delay and combining linear matrix inequality(LMI)techniques.Firstly,based on the time-delay segmentation method,the known time-delay interval is divided into two unequal sub-intervals.Secondly,the L-K functional with four-fold integral form is constructed on the interval with time-varying delay;Again,the third-order reciprocal convex combination method and the integral inequality method are applied to deal with the integral term of the functional along the time derivative.Finally,for the linear system with the interval time-varying delay,sufficient conditions of stability is obtained.And the validity of the conclusion is verified by numerical examples.3.On the basis of the second chapter,the problem of stability analysis of interval time-varying delay systems is studied in depth.Firstly,this paper generalizes the Wirtinger integral inequality to a new integral inequality.Secondly,this paper constructs an augmented L-K functional with a quadruple integral form,and use the new integral inequality of the triple integral type to process the integral term of the functional along the time derivative;Finally,the sufficient condition for the stability of the linear system with interval time-varying delays is obtained.The reasonable processing of the derivative integrals,which is neglected in the previous literature,has improved the existing stability conclusions to a certain extent.In theory,the stability criterion has less conservativeness,and verify the validity of the conclusions through numerical examples.At the end of this paper,the corresponding conclusions and prospects are made.