Research On Non-fragile Control For Periodic Piecewise Time-varying Systems

Periodic characteristics broadly exist in nature and engineering fields and have been studied and explored by scholars since the 19 th century.As a hybrid system with both periodic characteristics and switching characteristics,periodic piecewise systems have attracted wide attention in recent years because of their ability to describe the complex dynamic characteristics of periodic time-varying systems in detail.It consists of several time-invariant/time-varying subsystems,each of which has fixed dwell time and the switching order and runs repeatedly according to the periodic law.In addition to periodic piecewise system significant theoretical value,it has many applications in practical engineering,such as electrical and mechanical systems.At present,many research results have been made on the control for periodic piecewise system.However,the previous control schemes were designed on the assumption that the controller could be implemented accurately.In fact,in engineering applications,the parameters of the controller are often prone to slight perturbation or deviation due to their own or external factors,which leads to the deterioration of the controller performance or even damage to the system.Therefore,to guarantee the reliable operation and control for the periodic piecewise system,it is of great theoretical and engineering significance to design a robust non-fragile controller which can tolerate the uncertain gain perturbation of the controller.In this paper,the delay-dependent exponential stability,the finite-time extended dissipative,and the corresponding robust non-fragile controller design are studied based on the existing research on continuous-time periodic piecewise time-varying systems.The main contents are summarized as follows:1.In this paper,the stability and non-fragile stabilization problems are studied for periodic piecewise time-varying systems with time delays.Firstly,based on the Lyapunov-Krasovskii functional with periodic time-varying Lyapunov quadratic matrix,the exponential stability conditions related to time delay are obtained.Then,considering two kinds of norm-bounded uncertain controller gain perturbations,a non-fragile stabilization controller which can be solved directly based on the designed LMI.Compared with the previous work,the designed controller does not need to solve the gain based on the iterative algorithm,which reduces the complexity of the controller solution and improves its robustness,which is more beneficial to the engineering application.Finally,a numerical example is given to verify the effectiveness of the proposed scheme.2.The design of non-fragile H_?controller for the continuous-time periodic piecewise time-varying system is studied.Based on Lyapunov function with periodic time-varying Lyapunov polynomial matrix and2 L performance conditions,a periodic time-varying non-fragile H_?controller with higher degrees of freedom is designed,considering two kinds of uncertain controller gain disturbances with periodic time-varying matrix parameters.The controller is robust and can be solved directly based on LMI,which provides convenience for the performance optimization and control of the system.Finally,a numerical example is given to verify the effectiveness of the proposed scheme.3.The finite-time extended dissipative analysis and non-fragile extended dissipative control are studied for continuous-time periodic piecewise time-varying systems.Firstly,based on Lyapunov function with periodic time-varying Lyapunov quadratic matrix,sufficient conditions for finite-time boundedness and finite-time extended dissipative performance are obtained.Then,on this basis,two kinds of uncertain controller gain disturbances with periodic time-varying matrix parameters are considered,the non-fragile periodic time-varying controller with finite-time boundedness and optimal extended dissipative performance is designed.The designed controller is robust and can be solved directly based on LMI,which provides convenience for the performance optimization and control of the researched system.Finally,a numerical example is given to verify the effectiveness of the proposed scheme.