Finite Time Stability Of Switched Linear Systems Based On Switched Time-varying Lyapunov Function

As an important part of complex system and control science,switched linear systems are widely used in many fields,such as secure communication,traffic control,aircraft control and so on.Compared with the general systems stability analysis,the finite-time stability analysis of switched linear systems should consider not only the influence of switching signal on system stability,but also the running time of the system.Therefore,it is more complex than the stability study of general systems.At present,many domestic and foreign scholars have proposed a variety of research methods,but most of the results are obtained by using the average residence time and time-invariant Lyapunov function method.In this paper,the switched time-varying Lyapunov functions are designed for switched linear systems under different conditions according to the structural characteristics of the system and based on the mode-dependent range dwell-time switching signal,the new research results of finite time stability of the systems are given.The main work of this paper is as follows:In Chapter 1,the research background and significance of this research content are summarized,and the research status are analyzed.In Chapter 2,some basic symbols and definitions that used in this paper are given.In Chapter 3,for switched linear time-invariant systems,based on the mode-dependent range dwell-time switching signal,sufficient conditions for finite-time stability of the systems in continuous-time and discrete-time are given by constructing the switching time-varying Lyapunov functions.Numerical examples are given to prove the correctness of the results.Compared with the traditional Lyapunov functions,the design is more practical and easier to implement.In Chapter 4,on the basis of the previous chapter,uncertainty is introduced.For switched linear uncertain systems,some sufficient conditions for the finite-time stability of the systems in continuous-time and discrete-time are given by assuming different forms of uncertainty,based on the mode-dependent range dwell-time switching signal and using the switching time-varying Lyapunov functions.A data communication network transmission example and some numerical examples are used to prove the validity of the results.In Chapter 5,the disturbance is introduced into the systems that in the previous chapter.For switched linear uncertain systems with disturbance,sufficient conditions for the finite-time stability of the systems in continuous-time and discrete-time are obtained by assuming that the time-varying disturbance satisfies the corresponding conditions,based on the mode-dependent range dwell-time switching signal and using the switching time-varying Lyapunov functions.The validity of the results is verified by numerical simulations.In Chapter 6,the research results of this paper are summarized,the innovations and shortcomings are explained,and the possible future research topics are discussed.