H∞ control for singularly perturbed systems
This paper derives a set of ε-independent sufficient and necessary conditions for the H∞ 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∞ sub-optimal controller for the fast (slow) sub-system of the original system, respectively. ε-independent H∞ controller design is also considered. The main contribution of this paper is that our results apply to both standard and non-standard singularly perturbed systems.