Analysis And Control Of Fixed Dual Switching Discrete-time Linear System

The dual switching system is a special hybrid system,whose dynamic trajectory is affected by the deterministic switching signal and the stochastic switching signal.In recent years,the dual switching systems have been applied in the engineering fields of wind power generation,network control and other complex switching systems.Some scholars have carried out in-depth research on the stability analysis of the dual switching systems.However,due to the interaction between the dual switching signals and multiple subsystems,the stability of the dual switching systems become complex on the one hand.On the other hand,on account of the influence of various random noises and uncertainties,the stability analysis and controller design of the dual switching systems are more difficult.In this paper,based on the existing research results,the stability and control of dual switching system are studied in depth.The main work is summarized as follows:1.In view of the fixed dual switching discrete-time linear system with norm bounded uncertainties,based on the stochastic multi-Lyapunov function,the criterion of mean square stability of the system under the designed state-feedback switching law is given in the form of linear matrix inequality.Further,based on the above theoretical results,the sufficient conditions for the dual switching system to satisfy the H_?performance index are obtained.2.In view of the fixed dual switching discrete-time linear system with norm bounded uncertainties,the sufficient condition of exponential almost sure stability is obtained by designing the deterministic switching signal based on the stochastic multi-Lyapunov function.On this basis,the sufficient condition for the system to meet the H_?performance index is given.3.Aiming at the problem of switched stabilization design of fixed dual switched discrete-time linear systems,a comprehensive design of switched signal and state-feedback controller is carried out by using the principle of energy attenuation.Based on the stochastic multi-Lyapunov function,the sufficient conditions for the state-feedback stabilization of the system in the sense of mean square stability and exponential almost everywhere stability are given,and H_? performance index are satisfied respectively.