Delay-dependent L2-L∞ control of linear systems with multiple time-varying state and input delays

This paper is concerned with the L-2-L-infinity controller design problem for delayed linear systems. We first propose a novel class of continuous-time multiple delayed linear systems. The time-delays are assumed to be time-varying continuously differentiable functions, which appear in the state and control input simultaneously. By using the Lyapunov-Krasovskii functional approach and Jensen integral inequality technique, a sufficient condition for the existence of an L-2-L-infinity controller is formulated in the form of linear matrix inequalities (LMIs). When these LMIs are feasible, the L-2-L-infinity controller is explicitly presented. Finally, a numerical example is provided to demonstrate the effectiveness and feasibility of the developed controller design procedures. (C) 2011 Elsevier Ltd. All rights reserved.