Design Research For One-sided Lipschitz Lur'e Differential Inclusion Systems

With the development of science and technology and theoretical research,people's perception of the real world is more and more matured,and the considered actual control system is more and more complex.Differential equation can not be applied to describe the actual control system with uncertainty and discontinuity no longer,in the light of this situation,differential inclusion begins to be used to model and analyse the actual control system,and the differential inclusion system is also becoming the focus in academia.Meanwhile,as a kind of simple nonlinear systems,Lur'e differential inclusion systems become the starting point of researching nonlinear differential inclusion.Therefore,the research of Lur,e differential inclusion systems is a kind of scientific practice with important theoretical significance and application value.This paper investigates one-sided Lipschitz Lur'e differential inclusion systems mainly.Under the background of rotor system,the paper also simulates the numerical examples to show the effectiveness of all presented design methods.This paper mainly includes the following:Based on Lipschitz condition with unknown Lipschitz constant,an adaptive non-fragile controller is proposed.Then,Lipschitz condition is extended to one-sided Lipschitz condition,a new kind of non-fragile controller is presented by quadratically inner-bounded condition and S-procedure.Quadratically inner-bounded condition and S-procedure are used to study Lur'e differential inclusion systems with unknown parameters or Markovian jumping parameters.Under the one-sided Lipschitz condition,adaptive full-order observer and stochastic observer are designed for these systems respectively.In the condition of existence of full-order observer,reduced-order observer is also given by construction decomposition.Under the ?-one-sided Lipschitz condition,adaptive observer is designed by quadratically inner-bounded condition and S-procedure.Then,a corollary of 0-one-sided Lipschitz condition is also presented,and an adaptive observer is designed finally.The main contribution of this paper can be summarized as follows:1.Quadratically inner-bounded condition and S-procedure are employed to study Lur'e differential inclusion systems.This paper not only illustrates the simplicity and effectiveness of this method,but also possesses important significance of extension and generalization for Lur'e differential inclusion systems.2.Design methods of synchronization and observer for one-sided Lipschitz Lur'e differential inclusion systems are proposed,and the design methods may fill the gaps of synchronization and enrich the theory of observer design for Lur'e differential inclusion systems.3.?-one-sided Lipschitz condition is presented for the first time,and the condition is verified by theory proof and simulation verification.Based on ?-one-sided Lipschitz condition,cross term is extended to case where it is not Lipschitz.To some extent,this design method may overcome some disadvantages of adaptive observer design for one-sided Lipschitz nonlinear systems at present.