Stability Analysis Of Switched Positive Linear System Based On Time-varying Linear Co-positive Lyapunov Functions

As one of the most important classes of the hybrid dynamic systems,switched systems not only have important scientific value in the theoretical research,but also have a wide range of applications in practical engineering.On the other hand,since the state trajectory in the positive system is constrained in the nonnegative region of the state space,the positive system has a strong practical application background and theoretical research value in real life,which makes the positive system attract much attention.Compared with the positive system and the general switched system,the switched positive linear system has the characteristics of both the switched systems and the positive systems,which makes the study of the switched positive linear system more complicated and challenging.In recent years,switched positive linear systems has attracted the attention of researchers.As the basic nature of the systems,stability is first studied by people.So far,although some valuable research results have been obtained for switched positive linear systems,there are still many problems that need to be further solved.Based on the existing research results,this paper will further study the stability analysis of switched positive linear systems.The main contents are as follows:Chapter 1 is the introduction.It,summarizes the research significance,methods and existing achievements of the switched system,the positive system,the switched positive linear system,the interval uncertain positive linear system.Chapter 2 studies the uniformly exponential stability(GES)analysis for a class of switched positive linear systems under any switching signal with dwell time specifications.It is worth noting that.the dwell time of this chapter is different from the dwell time in the previous method.The dwell time of this chapter is an arbitrary prespecified constant,which is not computed by Lyapunov functions of the subsystems.It is known that the stability of the subsystem is not equal to the stability of the whole switched systems.Assuming that all subsystems are stable,for switched positive linear systems.The time-varying linear co-positive Lyapunov functions are proposed to study the exponential stability analysis.Firstly,when the dwell time is confined by a pair of upper and lower bounds,the sufficient conditions ensuring the exponential stability of switched positive linear systems are proposed by constructing the time-varying linear co-positive Lyapunov functions.Then,when the dwell time is confined only by the lower bound,the conditions on the uniformly exponential stability of the studied system are obtained.The proposed conditions can be formulated as the solutions on the linear programming problem,which is easy to check and suitable of the engineering application.Finally,the effectiveness of the proposed method is verified by a numerical example.Chapter 3 investigates the robust stability problem of switched positive linear systems with interval uncertainties Based on the time-varying linear co-positive Lyapunov function method proposed in the second chapter,we further study the robust stability analysis of a class of interval uncertain switched positive linear systems under a given dwell time switching signal.Firstly,we advance an arbitrary constant as the dwell time for switched positive linear systems.Secondly,by constructing certain new piecewise time-varying linear co-positive Lyapunov function,computable sufficient conditions for stability analysis of a class of the interval uncertain switched positive linear systems under the two conditions of satisfying upper and lower bound constraints and only lower bound constraints,we restrict the growth of Lyapunov function for the actively operating subsystem,thus forcing "energy" of the overall switched system to decrease at the switching instants.The proposed conditions can be formulated as the solutions on the linear programming problem,which is easy to check and suitable of the engineering application.Finally,an example is presented to demonstrate the effectiveness of the proposed method.Chapter 4 summarizes the main research contents and conclusions,and perspectives end the dissertation.