Stability Analysis And Control Synthesis Of Switched Systems Based On Transferring-dependent Lyapunov Function

Switched system consists of switching signal and subsystems.The evolution of system state not only relies on the switching signal,but also relies on the dynamic characteristics of each subsystem.Up to now,switched system has grabbed the attention of numerous theoretical researchers;meanwhile,it has been applied to varied practical fields,such as power systems,robot systems.In recent years,the method combining Lyapunov function and time dependent switching is mainly used in the research of switched systems.Therefore,this thesis proposes two novel Lyapunov functions,which are transferring dependent convex Lyapunov function and transferring dependent Lyapunov function.The novelty of the two Lyapunov functions is that they are constructed in a way that not only depends on the currently activated system mode,but also depends on the freshly deactivated system mode.Next,the stability and control synthesis of switched systems are studied by adopting two new Lyapunov function approaches and admissible edge dependent average dwell time switching technique.The main contents are summarized as follows:First of all,the approaches of transferring dependent convex Lyapunov function and transferring dependent Lyapunov function are proposed for continuous time switched systems with admissible edge dependent average dwell time switching.The transferring dependent convex Lyapunov function is made up of a series of convex functions and positive definite matrices,which can greatly relax restricted conditions of Lyapunov function at the switching points so as to obtain a larger stability region.Based on the Lyapunov functions,two transferring dependent controllers are designed to ensure the stability of the closed loop system.In the end,a numerical example is provided to verify the effectiveness of the designed Lyapunov functions in the aspect of stability analysis;a tunnel diode circuit is employed to unfold the potency of the above controller design approaches in optimizing control performances.The two transferring dependent Lyapunov functions designed above are extended to the discrete time domain.Then,via the slow/fast admissible edge dependent average dwell time switching technique,the problems of stability and controller design for discrete time switched systems with unstable subsystems are studied.Compared with previous results,the less conservative stability criteria are obtained.Furthermore,the transferring dependent convex controller and transferring dependent traditional controller are devised to ensure the global uniform exponential stability of the closed loop system.Finally,the effectiveness of the proposed approach is verified by two numerical examples.Then,the stability and control issues are investigated for discrete time switched system involoving finite time stability,finite time boundedness and finite time H_∞ control.Based on the transferring dependent convex Lyapunov function and the transferring dependent Lyapunov function method,a series of improved finite time stability results are obtained under the admissible edge dependent average dwell time switching technique.Based on this,transferring dependent convex controller and transferring dependent traditional controller are established,which guarantee the finite time boundedness with H_∞ performance of the closed loop systems.Finally,two numerical examples and an application example are used to verify the effectiveness and superiority of the proposed transferring dependent controller design approaches.Asynchronous l₂-l_∞ filtering is researched for discrete time switched systems.An admissible edge dependent integrated dwell time is proposed and an asynchronous transferring dependent convex Lyapunov function is designed.The Lyapunov function switching does not depend on the system mode,but depends on the currently activated filter mode and the freshly deactivated filter mode.Based on this,the sufficitient conditions are derived to ensure the global uniform exponential stability and l₂-l_∞ performance of the filtering error system.Meanwhile,the method of constructing asynchronous l₂-l_∞filter is given.A numerical example and switched RLC application circuit are given to demonstrate the potential and validity of the proposed results.