H∞-control design for systems with multiple delays

Abstract

In this paper, H ∞-control design is developed for a class of linear dynamical systems with multiple state and input delays. Both the asymptotic stability conditions and the H ∞-norm bound of the closed-loop transfer function are established. Feedback control synthesis is developed using state feedback. In addition, when the class of linear systems with multiple state and input delays undergoes norm-bound uncertainties, H ∞-control synthesis is established. The developed results are conveniently cast into linear matrix inequality (LMI) framework. Simulation examples are given to illustrate the theoretical developments.