H∞ control for singularly perturbed systems with parametric uncertainties

This paper studies the problem of robust control of a class of singularly perturbed linear continuous-time systems with parameter uncertainty. First, under certain conditions, we derive a stabilizing and γ-attenuating controller for the singularly perturbed nominal system for all ε ∈ (0, ε₁]. Then our attention is focused on the design of a composite linear controller based on the slow and fast problems such that both robust stability and a prescribed H_∞ performance for the full-order system are achieved, irrespective of the uncertainties