Observer Design For A Class Of Switched Systems With Unknown Inputs

Switched systems are a class of hybrid systems with complex dynamic characteristics,which have become an international frontier in the theoretical research of hybrid systems because of their extensive practical application background and important research value.Observer design is one of the important issues to be considered in practical switched systems.When there are unknown inputs in the switched systems,the observer design of the systems is usually much more complicated than that of the general switched systems.Therefore,it is of great scientific significance and extensive practical application value to study the observer design problem of switched systems with unknown inputs.Although there have been many excellent results in the study of observers for switched systems,the research on the design of observers for switched systems with unknown inputs whose subsystems do not have strong detectability is not yet comprehensive.In this paper,in the design of the switched systems observer,reduced-order observer is constructed,which reduces the dimension of the observer and makes the observer structure simpler,and introduces a double time-varying function into the Lyapunov function to construct a Lyapunov function containing the information of the switching energy drop rate,so that the proposed Lyapunov function does not have to be double-dropped,but only needs to drop in energy at the switching instant.The main work of the paper is summarized as follows:In chapter 1,firstly,the switched systems are reviewed,and then the research significance,methods and progress of the switched systems with unknown input are summarized.Finally,the main content and framework of this paper are briefly introduced.In chapter 2,this chapter investigates the reduced-order switched observers for switched linear systems with unknown inputs when none subsystems are strongly detectable under dwell time switching.A time-varying disturbance-decoupling state coordinate transformation is first utilized to decouples the unknown input from a subset of the transformed state coordinates.Secondly,a linear coordinate transformation is constructed to decompose the system state into directly available state component parts and non-direct available state component parts.The existence conditions of the reduced-order switched observers are derived by both restricting the upper bounds and the lower bounds of dwell time,decreasing the energy of switched systems at switching times,and confining the growth of subsystems' Lyapunov functions,and the reduced-order switched observers are constructed.Stability analysis of switched error dynamics is also presented.Then,the proposed reduced-order switched observers asymptotically converges to the state under the designed dwell time switching signal.Finally,an example confirms the effectiveness of the proposed method.In chapter 3,on the basis of the second chapter,the observer design problem of the unilateral Lipschitz nonlinear system with unknown inputs are studied.In this chapter,A time-varying disturbance-decoupling state coordinate transformation is first utilized to decouples the unknown input from a subset of the transformed state coordinates.Second,a new method based on dwell-time switching signals and linear matrix inequalities is proposed to design a reduced-order observer for this system.The sufficient conditions to guarantee the existence of the reduced-order observer are obtained.Then,Stability analysis of switched error dynamics is also presented.Finally,an example confirms the effectiveness of the proposed method.In chapter 4,summarize the main work of the paper,and look forward to the next research work.