Robust ℓ∞ stabilization under data rate constraints

This paper is concerned with robust stabilization of an uncertain system over a rate-limited digital channel from the viewpoint of input-output stability. Because of the quantization in the communication channel, it is impossible to apply the traditional small gain theorem to establish robust stability of the feedback system. To overcome this difficulty, we introduce a new notion of small lscr^infin signal lscr^infin stability, and derive a sufficient robust stability condition against lscr^infin gain-bounded uncertainty based on this notion. Furthermore, for the case of a scalar nominal system, a sufficient data rate for the existence of a robustly stabilizing encoder-controller pair is explicitly given.