Analysis and design of ℋ_∞ feedback control systems with two quantized signals

In this paper, we consider analysis and design of ℋ_∞ feedback control systems with two quantized signals. We assume that a state feedback has been designed for a continuous-time LTI (linear time-invariant) system so that the closed-loop system is Hurwitz stable and a desired ℋ_∞, disturbance attenuation level is achieved. However, 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 and achieves the same ℋ_∞ disturbance attenuation level. We also extend the discussion to the case of static output feedback where the measured outputs are quantized.