Research On Interval Observer Design For Switched Systems

With the development of control theory,the considered system has become more and more complex,and it has been more and more difficult to obtain the information of system state.However,the system state has irreplaceable advantages in terms of stabilization,decoupling,and tracking problems in the system.Therefore,the concept of state reconstruction,that is,state observer,was proposed.It was first verified in linear systems,and then widely used to study various synthesis problems.After that,great progress has been made in the investigation of state observers.Various forms have emerged numerously,and design methods have been diverse.Among these proposed observers,interval observers known as a class of disturbance attenuation observers have drawn considerable interest of the researchers.Meanwhile,hybrid systems are always a big mountain standing in front of control theory researchers.Naturally,it has also become the hot topic in the field of control theory.As an important class of hybrid systems,switched systems have received more and more attention in recent years.Therefore,the research of interval observer design method for switched systems has important theoretical significance and practical application value.The main research object of this paper is the switched system.Based on this,effective interval observer design methods are proposed,and the designed interval observer is verified by simulations.The main research contents of this paper are as follows:1.For linear switched systems with uncertain terms,a new type of interval observer is designed by combining the H? observer design method with the zonotope method2.Considering that the interval observer is not synchronized with the switched system,the observer design method and the zonotope method are used to design an interval observer for asynchronous switched systems.3.Based on the linear programming method,the interval observer design methods for linear and non-linear switched systems are proposed respectively,and multiple linear cooperative Lyapunov function is used to prove the theory.4.The research objective is generalized to switched systems with uncertain terms,and the finite-time stability theory is introduced.Based on the linear programming method,a finite-time interval observer for a class of switched systems is designed.The main innovations of this paper are as follows1.Zonotope method is introduced into the problem of designing interval observers,which solves the problem that most current interval observers need to satisfy the conditions of the existence of the gain L such that the error system is positive,or use the coordinate transformation to transform when it is not satisfied.The conservatism of design is reduced,and the accuracy of the observer is also improved.2.Asynchronous theory is applied to the interval observer design for switched systems,and a method of designing asynchronous interval observers for switching systems is proposed.The scope of application of interval observer design method is expanded,and the interval observer design theory is enriched.3.Combining positive system theory with finite time stability theory,a finite time observer design method for switched systems is given based on linear programming method.It overcomes the limitation that the error bound can not be kept within a specific time.The applicability of the interval observer is also enhanced.