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

The observer design problem has attracted wide attention by researchers.Moreover,the order of the funct,ional observer may be smaller than that of the state observer,so it is of great practical significance to study the functional observer design for nonlinear systems.This paper considers the functional observer design problem for a class of nonlinear systems and time-delay nonlinear systems with incremental quadratic constraints.The main research contents are as follows.First,a functional observer design for the nonlinear systems with incremental quadratic constraints is studied.Based on Moore-Penrose pseudo-inverse and linear matrix inequality theory,the existence conditions of the functional observer are obtained.Moreover,exponential convergence of the estimate errors can be achieved.Through the Lorenz system,it is illustrated that the proposed approach can provide a smaller order of observer than that of the conventional approaches,while maintaining satisfactory performances.Secondly,a functional observer design for the time-delay nonlinear systems with incremental quadratic constraints is investigated.Sufficient conditions ensuring the exponential stability of the functional observer are established and formulated in terms of linear matrix inequalities.By constructing a Lyapunov-Krasovskii functional,the exponential convergence of the estimate error dynamics is achieved.The effectiveness of the proposed design approach is illustrated by an example.