Exponential Stabilization And Robust H-infinity Control For A Class Of Switched Singular Time-delay Systems

In recent years,a class of systems which corresponds with the normal system with extensive form has been paid special attention by a lot of domestic and overseas researchers because the modern control theory and method are used widely in engineering system and the other field of learning.It is called singular system.The delay and the uncertain phenomenon are also considered so that this mode can get closer to the actual system.Now the research results about switched singular time-delay systems are not much,so there are still many theoretical and practical problems to be solved.Therefore,it has important practical value for the further researches of switched singular time-delay systems.Using average dwell time approach,parameter adjustment method and free-weighting matrices method,this paper constructs singular Lyapunov-Krasovskii function to research exponential stabilization and robust H-infinity control for a class of switched singular time-delay systems.This paper is summarized as follows:(1)The problem of exponential stabilization for a class of switched singular time-delay systems is studied.Firstly,we discuss the exponential admissibility problems of the switched singular time-delay systems so that the systems are regular,impulse free,and exponentially stable.Then,on that basis,mode-dependent state-feedback controllers of the corresponding closed loop systems are considered and designed.The solution of linear matrix inequalities can solve the controllers easily.(2)The problem of the H-infinity exponential admissibility problems and exponential stabilization H-infinity control problems of switched singular time-delay systems are studied.Using average dwell time and free-weighting matrices approaches,the sufficient condition of switched singular time-delay systems H-infinity exponential admissibility is given.On that basis,state-feedback controllers which make the corresponding closed loop systems exponentially admissible are design and the obtained matrix inequalities are transformed into the linear matrix inequalities.Numerical example is given to illustrate the validity and feasibility of the results.(3)The problem of exponential stabilization and robust H-infinity control for a class of switched singular time-delay systems are studied.Firstly,we discuss the robust H-infinity and exponential admissibility problems of the switched singular time-delay systems using average dwell time and free-weighting matrices approaches.Then,on that basis,the state-feedback control problem is considered.Using the linear matrix inequality method,mode-dependent state-feedback controllers of the closed loop systems are designed so that the systems are exponentially admissible.And numerical example is given.