Output Tracking And Regulation Problem Of Switched Time-Delay Systems Based On Incremental Passivity

The output tracking and regulation control problem of switched time-delay systems is of great significance in both theoretical research and practical application,and the incremental passivity theory also plays an important role in the study of output tracking and regulation control problem of switched systems.However,there is a common time-delay in many practical systems.For the switched time-delay systems,the incremental passivity theory is not applied to solve the control problem.In this paper,we propose the definition of incremental passivity for switched time-delay systems,and discuss the output tracking and regulation control problem of switched time-delay systems based on the incremental passivity.We initially establish a basic theoretical framework of control problem for such switched time-delay systems based on the incremental passivity.The main work of this paper is as follows:First,the definition of incremental passivity for a class of switched time-delay systems is proposed.Without assuming that the subsystems is incremental passive,a multiple Lyapunov function method is used to design the switching rules,and a sufficient condition for the incremental passivity of switched time-delay systems is given in the form of LMIs.As a special case,in the case of parameters with special values,a switched time-delay systems with input and output incremental passivity is also discussed.Combining the Wirtinger integral inequality and the Finsler lemma to deal with the time-delay term,the calculation process is simplified,and the conservation of the main results is reduced.Secondly,based on the output incremental passivity,the output tracking problem of a class of switched time-delay systems is discussed.For the switched time-delay systems with output incremental passivity,based on the multiple Lyapunov function method,the error feedback controller and the state-dependent switching rules are designed to give the solvability of the output tracking problem for switched time-delay systems without requiring that output tracking problem of subsystems be solvable.Finally,the output regulation problem for a class of switched time-delay systems is discussed based on the output incremental passivity.First,we construct a switched time-delay internal model controller.And using the multiple Lyapunov function method to design the switching rules,a sufficient condition for the output incremental passivity of the switched time-delay internal model controller is given.Then,the sufficient condition for the solvability of the output regulation problem of a closed-loop systems with feedback connection betweena switched time-delay controller and a controllable systems is given in the form of LMIs.Among them,the switching rule of the switched time-delay internal model controller is different from that of the controlled switched time-delay systems.That does not require synchronous switching between the two.Therefore,there is greater freedom in design.