Stability of quantized control systems under dynamic bit assignment

In recent years, there have been several papers characterizing the minimum number of quantization levels required to assure closed-loop stability. This minimum bit rate is usually achieved through time-varying quantization policies. Many networks, however, prefer a constant bit rate configuration, so it is useful to characterize the stability of quantized feedback systems under constant bit rate quantization. This note first derives a lower bound on the number of quantization levels required for closed-loop stability under constant bit rates. We then introduce a novel dynamic bit allocation policy that achieves this bound.