Stabilization of LTI Systems with Quantized State-Quantized Input Static Feedback

This paper is concerned with the stabilization problem for discrete-time linear systems subject to a uniform quantization of the control set and to a regular state quantization, both fixed a priori. As it is well known, for quantized systems only weak (practical) stability properties can be achieved. Therefore, we focus on the existence and construction of quantized controllers (mapping a quantized state into a quantized input set) capable of steering a system to within invariant neighbourhoods of the equilibrium. Such analysis is helpful because it allows to decide a priori whether adesired control objective can be achieved by using a \textit{given} technology (actuators, sensors, communication and computational means).