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

This paper is concerned with the L2–L∞L2–L∞ 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 L2–L∞L2–L∞ controller is formulated in the form of linear matrix inequalities (LMIs). When these LMIs are feasible, the L2–L∞L2–L∞ controller is explicitly presented. Finally, a numerical example is provided to demonstrate the effectiveness and feasibility of the developed controller design procedures.