State feedback and static output feedback for discrete-time LTI systems with two quantized signals

Quantized feedback control have received a lot of attention in recent years. In this paper, we consider the analysis of state feedback and static output feedback for the discrete-time LTI (linear time-invariant) systems with two quantized signals. We assume that the state feedback and static output feedback have been designed for a discrete-time LTI system so that the closed-loop system is Hurwitz stable. It is assumed that the states are quantized before they are passed to the controller, and the control inputs are quantized before they reach the system. For such quantized feedback control systems, we propose a state-dependent strategy for updating the quantizers´ parameters, so that the system is asymptotically stable. We also extend the discussion to the case of static output feedback where the measured outputs are quantized.