Finite-time Stabilization Of Singular Linear Systems

Singular system is the basic model in the field of system and control science,which has been widely used in many engineering fields.For the finite-time stability analysis of singular linear systems,it is necessary to consider the finite-time stability of the system and other issues such as regularity of the system.Therefore,compared with the general system,the stability of singular linear systems is more complex.At present,although there are a lot of results aimed at finite-time stability of singular linear systems,most of them are presented by using time-independent Lyapunov functions.This paper uses the structural characteristics of the singular linear system to design a class of time-dependent Lyapunov function,gives new conditions for the finite-time stability of the singular linear system,and try to reduce the conservatism of the results.This paper is divided into the following six chapters.In Chapter 1,the background of singular systems,switched singular system and finite time stability are introduced.In Chapter 2,some commonly used symbols and basic concepts are presented.In Chapter 3,as for the finite-time stability of continuous-time singular linear systems,by constructing a class of time-dependent Lyapunov functions and introducing a zero term with free weighting matrices,new explicit conditions are given in terms of linear matrix inequalities,which do not contain unsolvable matrix differential inequalities,then,it is extended to theH_?finite time stability of the system,and also considers the finite-time stability of discrete-time singular linear systems.Finally,the examples are given to illustrate the effectiveness and conservatism of the method.In Chapter 4,similar to the method in Chapter 3,finite-time stability of continuous-time singular linear time-delay systems is studied,and the finite-time stability of discrete-time is also considered.Finally,numerical examples are given to verify the effectiveness and conservatism of the results.In Chapter 5,by means of multiple time-varying Lyapunov function and mode dependent average dwell time method,the sufficient conditions for the finite time stability of switched singular linear system are given,furthermore,the sufficient conditions for theH_?finite time stability of the system are given.Finally,the examples are given to prove the feasibility of the results.In Chapter 6,the main contents of the paper are summarized,and look forward to new possible research topics.