\(H_\infty\) control for singularly perturbed systems (Q1129694)

This paper derives a set of \(\varepsilon\)-independent sufficient and necessary conditions for the \(H_\infty\) control problem for singularly perturbed systems in a different approach from previous ones. A sub-optimal controller is explicitly constructed. We observe that the controller is also singularly perturbed, with its fast (slow) part being an \(H_\infty\) sub-optimal controller for the fast (slow) sub-system of the original system, respectively. \(\varepsilon\)-independent \(H_\infty\) controller design is also considered. The main contribution of this paper is that the results apply to both standard and non-standard singularly perturbed systems.