Input-to-state stabilization with minimum number of quantization regions

We study control systems where the state measurements are quantized and time-sampled, and an unknown disturbance is being applied. We present a dynamic quantization scheme that switches between three modes of operation. We show that by using this scheme with a continuous static feedback controller we achieve a closed-loop system which has the Input-to-State Stability property (ISS). Our design does not use any characterization of the disturbance; as long as the disturbance is bounded the system will remain stable. We show that three quantization regions per dimension is sufficient to achieve the ISS property, and furthermore we show that the ISS property is achievable using a data rate that is arbitrarily close to the minimum required data rate when no disturbance is applied.