Research On Finite-time Control And Filtering For Switched Systems Under Edge-dependent Switching

The progress of science and technology leads the development of society and puts forward higher requirements for intelligent control.As a kind of dynamic system composed of continuous dynamic subsystem and discrete dynamic subsystem,hybrid system is favored by experts and scholars at home and abroad.As a special class of hybrid systems,a switched system is generally composed of a family of subsystems and a switching signal which orchestrates the switching between them.It has always been a hot topic and important model for the study of hybrid systems at home and abroad.In the research process of switching system,stability analysis and control synthesis are its key points and difficulties.Primarily,people focused on the Lyapunov asymptotic stability and control synthesis of switched systems.However,in practical engineering applications,the dynamic behavior of switched systems in the finite-time intervals,that is,finite-time stability,is also a hot issue worthy of attention.Therefore,this paper will study the discrete-time switched linear systems from the aspects of finite-time stability,finite-time boundedness,finite-time H∞ control synthesis and finite-time H∞ filtering design.The main research contents and results are as follows:Firstly,this paper study the finite-time stability for a class of discrete-time switched linear systems by using the multiple discontinuous Lyapunov function analysis method,and establish the solvable stability conditions based on linear matrix inequalities（LMIs）.After that,the sufficient conditions of the finite-time boundedness for the discrete-time switched linear system with norm-bounded external disturbance are analyzed.We further study the sufficient conditions for the finite-time stabilization of the discrete-time switched linear systems by designing a set of state feedback controllers under the constraints of the admissible edge-dependent average dwell time（AED-ADT）switching signals.Secondly,based on the analysis of finite-time stability and finite-time boundedness obtained above,this paper study the finite-time H∞ performance of the system with the external disturbance by combining the multiple discontinuous Lyapunov function technique and the AED-ADT method.At the same time,a finite-time H∞ controller is designed,which makes the discrete-time switched linear system is finite-time boundedness and achieves a prescribed H∞ performance index with the constraints of the AED-ADT switching signals.In addition,a numerical example is used to highlight the superiority and effectiveness of the AED-ADT switching compared with the traditional mode-dependent average dwell time（MDADT）switching.Meanwhile,a classical DC-DC power converter circuit example is used to verify the practicability of the conclusion obtained in this paper.Finally,the problem of the finite-time H∞ filtering design for the discrete-time switched linear systems is investigated.Combining the AED-ADT method and multiple discontinuous Lyapunov function technique,the sufficient condition of finite-time boundedness for the filtering error system is analyzed and a set of finite-time H∞ filter is deisgned.Then,a numerical example is given to illustrate the effectiveness and superiority of the AED-ADT method compared with the traditional MDADT approach.At the same time,a practical circuit example is exhibited to verify the practicability of the results obtained in this paper.