Robust H∞ control of uncertain distributed delay systems

This paper presents delay-dependent robust H_∞ controller design for a class of uncertain linear systems with a time-varying discrete delay and a constant distributed delay. The parameter uncertainties are assumed to reside in a polytope. Designing a linear memoryless state feedback H_∞ controller, and a sufficient condition with delay-dependent is derived for the robust asymptotic stability of the closed-loop systems in terms of linear matrix inequalities (LMIs) by applying the parameter-dependent Lyapunov functional approach. The desired controller can be found by solving a convex optimization problem. The proposed methods can be easily extended to the case of multiple time delays. A numerical example is included to demonstrate the effectiveness of the proposed methods.