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Stability Analysis For Several Classes Of Linear Systems Witn Time-delay

Posted on:2018-11-12Degree:MasterType:Thesis
Country:ChinaCandidate:Y XieFull Text:PDF
GTID:2348330533963643Subject:Computational Mathematics
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Time-delay is a kind of widespread physical phenomena in many practical realities and engineering systems,such as biological systems,economic systems,process control,and networked control systems,etc.Time delay phenomena appears in many dynamic systems which inevitably makes the whole system performance index declined,and even leads to system instability.Therefore,the study of stability problem of time-delay system attracted the attention of the experts and scholars and emerged many outstanding research results.There are many kinds of systems with time delay and different systems may exhibit different properties,so it has a practical significance to study the different types of time delay system.This thesis is concerned with the analysis of stability of three types of linear time delay systems.By using the Lyapunov-Krasovskii stability theory and linear matrix inequalities methods,the stability criterions of several typical time-delay systems are obtained.Comparing with the existing results,this thesis has better conservative.The main results of this paper are as follows:Firstly,for singular systems with constant time delay,by representing the singular system as a neutral form,using an augmented Lyapunov-Krasovskii functional and the Wirtinger-based double integral inequality.In addition,a sufficient condition in terms of linear matrix inequalities is given to guarantee system stable.Secondly,for singular systems with interval time-varying delays,a delay-derivative dependent stability criterion is given in terms of linear matrix inequalities which can produce allowable delay bounds as large as possible and the number of decision variables as few as possible.The main techniques are the Wirtinger-based double integral inequality and augmented Lyapunov functional method that employs much delay information.Several classical examples show the effectiveness and merits of the method.Finally,for linear systems with distributed delays,by combining with the lyapunov stability theory,and involving technology includes Wirtinger double integral inequality,Lyaponov direct method and other methods in the treatment of the functional derivative term,a sufficient condition in terms of linear matrix inequalities is given to guarantee linear systems with distributed delays stable.
Keywords/Search Tags:Linear time-delay system, Wirtinger double integral inequality, equivalent system approach, linear matrix inequality, stability
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