A new framework for robust stability analysis of quantized feedback systems

In this paper, a novel framework for robust stability analysis of quantized feedback systems is developed. For an uncertain quantized feedback system, it is difficult or sometimes impossible to employ the traditional small gain theorem to establish the robust stability of the feedback system: if the nominal part of the feedback system has a signal with finitely many quantization levels in the feedback loop, it is sometimes impossible to make it be finite gain ℓ^p stable. Furthermore, it is often too conservative to approximate the nonlinearity of the system including quantization errors with the traditional ℓ^p gain bounded uncertainty. For such quantized feedback systems, we introduce a new stability notion of small ℓ^p signal ℓ^p stability and derive conditions for robust stability of the feedback system based on this stability notion. We also give two illustrative examples to show the usefulness of the proposed framework for the stability analysis of some classes of quantized feedback systems.