Stability of nonlinear continuous time systems with memoryless digital controllers

This paper presents results on the stability of hybrid systems which are continuous-time nonlinear systems with a digital controller. Existence and uniqueness results for quantized systems are presented. The main result of the paper shows that there exists a sampling time and quantization step such that the closed-loop system is uniformly and ultimately bounded given any arbitrary bound. An extension of the classical Lyapunov theorem is given to analyze this class of hybrid systems. The digital control scheme includes sampling (possibly multirate), quantization and reconstruction by a zero-order hold.