Adaptive Control Of Several Switched Singular Systems

With the development of science and technology,switched singular systems as an important hybrid system are more and more applied in practical fields,and adaptive control is one of the methods to solve the problem of system control design.Adaptive control of switching systems has been widely studied and fruitful results have been achieved.Switched singular systems is a further extension of normal switching system and has profound theoretical and practical significance.In this paper,the adaptive control of several switched singular systems is studied by means of Lyapunov's basic theory of stability and linear matrix inequality and by constructing proper Lyapunov function.The main research work is as follows:1.For a class of linear switched singular systems,the adaptive state feedback control problem is studied by using linear matrix inequality and lyapunov stability theorem.Firstly,the adaptive law of the system is given by combining the Lyapunov function and some inequality techniques,and sufficient conditions for the stability of the system are proposed.Then,the tracking problem of the system is analyzed,and finally the simulation results are given.2.For a class of nonlinear switched singular systems satisfy Lipschitz condition,study the adaptive state feedback control design problem,the first by a single input nonlinear switched generalized Lyapunov stability theorem sufficient conditions for the robust stability of the system,which has been generalized to multi-input nonlinear generalized switching system adaptive tracking problem,finally the simulation results prove the above theory.3.For a class of uncertain switched singular systems,robust adaptive feedback control is studied.Based on the model reference adaptive control method and the multi-lyapunov function method,a switched adaptive controller for uncertain switched singular systems is proposed.To ensure the stability of the closed-loop switching system,sufficient conditions for the stability of the system are derived based on linear matrix inequality(LMI).