Functional observer design for nonlinear systems with incremental quadratic constraints

Abstract

We present a functional observer design method for a class of nonlinear systems with output nonlinearities and incremental quadratic constraints. The system under consideration includes a wider class of nonlinear systems, such as, Lipschitz, one-sided Lipschitz, nondecreasing nonlinearity system as special cases. Based on Moore–Penrose pseudo-inverse and linear matrix inequality theory, the existence conditions of gain matrices of a functional observer are obtained. Moreover, exponential convergence of the estimate errors is achieved. Through the Lorenz system, it is shown that the proposed approach provides a smaller order of observer than that of the conventional approaches, while maintaining satisfactory performances.