Functional Observer Design For A Class Of Discrete-time Nonlinear Systems With Incremental Quadratic Constraints

Observer design for discrete-time nonlinear systems has always attracted researchers.In particular,the order of the functional observer is often lower than that of state observer.Therefore,it is of great practical significance to investigate the functional observer of discrete-time nonlinear systems.This paper mainly investigates the functional observer design for a class of discrete-time nonlinear systems with incremental quadratic constraints.The specific research contents of this paper are as follows:Firstly,functional observer design for a class of nonlinear discrete-time systems satisfying incremental quadratic constraints is investigated.By using Lyapunov stability theory,matrix equation rank condition and linear matrix inequality method,the sufficient conditions for the exponential convergence of the observation error of the functional observer and the design method of the gain matrix are obtained.An example is given to illustrate the effectiveness of this design method.Secondly,functional observer design for a class of nonlinear discrete-time systems with time-delay satisfying incremental quadratic constraints is studied.Then sufficient conditions for the design of functional observer and the construction of gain matrix for a class of discrete-time nonlinear systems with time-delay are derived which based on Lyapunov stability theory,Schur’s complement lemma and linear matrix inequality technique.A simulation example is also given to verify the feasibility and effectiveness of the proposed design.