Observer based delay-dependent robust H∞ control of nonlinear uncertain systems with state and input delays

Observer-based delay-dependent robust H_∞ controller design problem for state and input time-delays systems with a class of nonlinear uncertainties is discussed in this paper. Assuming that the nonlinear uncertain functions in the considered model are gain-bounded, we obtain a sufficient condition for robustly asymptotic stability and H_∞ performance of the closed-loop system in the light of Lyapunov stability theory. By solving a pair of linear matrix inequalities (LMIs), we construct delay-dependent state feedback control law which guarantees robustly asymptotic stability of the closed-loop system and reduce the effect of the disturbance input on the controlled output to a prescribed level. The delay-bounds and the H_∞ performance bound can be optimized. A numerical example is given to illustrate our results.