A robust H₂/H_∞ control approach to uncertain systems with time-varying delays

Abstract

An efficient descriptor approach is developed to solving the robust mixed H 2 =H ? control design problem for a class of linear uncertain systems with time-varying delays. The rationale behind this approach is to exhibit the delay dependence dynamics in the design procedure with an injected relaxation variable. Therefore, the need for overbounding crossproduct terms is bypassed. In the system under consideration, the delay factor is an unknown differentiable function and the uncertainties are assumed to be real, time varying, and norm bounded. A state feedback control is derived for both nominal and uncertain systems such that the H 2 performance measure is minimized while guaranteeing a prescribed H ? norm bound on the controlled system. All the developed results are cast in the format of linear matrix inequalities (LMIs), and a detailed numerical example is presented to illustrate the theoretical analysis.