Filter Design Problem For A Class Of Switched Systems With Time-varying Delay

The switched systems are a class of typical hybrid systems.Different from other systems,the structure of switched systems is composed of multiple subsystems,the switched modes between subsystems will have certain influence on the stability of the systems.Therefore,the design of switched rules is of significant.This paper investigates the stability of the switched systems by utilizing the average dwell time method and exponential stability method to study.On the other hand,the filterhas been widely used in industrial production because of its low demand for interference signal and its ability to deal with the uncertainty of system parameters.At the same time,the time delay problem has attracted the common attention of many scholars,the delay includes two cases,one is the state delay,the other is the asynchronous phenomenon between the subsystem and the controller.This paper discusses the exponential stability of different switching systems with time delay and the design of filter.The main research contents are as follows:1.In order to solve the problem of fault detection of continuous switching system,a fault detection filter satisfying the performance index is designed.Firstly,a fault detection filter is constructed to obtain the residual,and a performance index which can reflect the robustness of the residual on the disturbance and the sensitivity of the fault is introduced,and the problem of the solution filter is converted into the optimization problem.Next,the designed augmented filtering error switchingsystem is exponential and has the performance level,which is verified by usingthe Lyapunov function method and the average dwell time technique.Finally,on the basis of this,the existence conditions of the solution of the filtering design problem and the method of solving the gain matrix and the weight matrix of the designed filter are given,and the solution is expressed as a linear matrix inequality.2.The exponential stability of a linear switching system with time-varying time-delay under asynchronous switching is studied,and a filter design problem with performance index is designed.Firstly,using the Lyapunov stability principle,thefilter structure of the Lyapunov function and the switching system is designed.It is verified that the augmented filter error switching system designed under asynchronous switching is stable and has performance level.The Lyapunov function isdetermined by the switching signal of the filter.On this basis,the filter designmethod of the switching system is proposed.In addition,combining the linear matrix inequality method to solve the filter design problem,the problem is reduced tolinear matrix inequality.Finally,some numerical simulations prove the validity and reliability of the conclusion.3.The robust stability of a linear switching system with constant delay with uncertainty under asynchronous switching is studied,and a filter design problem with performance index is designed.First,using the Lyapunov function and the filterstructure of the switching system,it is verified that the augmented filter error switching system designed under asynchronous switching is exponential stable and has performance level.The designed Lyapunov function is determined by theswitching signal of the filter.The uncertainty in the switching system is processed.The filter design problem is solved by combining the linear matrix inequalitymethod.The problem is reduced to the linear matrix inequality.