Delay-dependent robust H _∞ controller design for a class of nonlinear uncertainty time-delay systems with input delay

Abstract

Based on an appropriate Lyapunov function, this paper analyzes the design of a delay-dependent robust H _∞ state feedback control, with a focus on a class of nonlinear uncertainty linear time-delay systems with input delay using linear matrix inequalities. Under the condition that the nonlinear uncertain functions are gain bounded, a sufficient condition dependent on the delays of the state and input is presented for the existence of H _∞ controller. The proposed controller not only stabilized closed-loop uncertain systems but also guaranteed a prescribed H _∞ norm bound of closed-loop transfer matrix from the disturbance to controlled output. By solving a linear matrix inequation, we can obtain the robust H _∞ controller. An example is given to show the effectiveness of the proposed method.