A Necessary and Sufficient Feedback Dropout Condition to Stabilize Quantized Linear Control Systems With Bounded Noise

This technical note studies the almost sure input-to-state stability of quantized linear systems with bounded noise under nondeterministic feedback dropouts. It proposes a dropout condition which is both necessary and sufficient for stabilizing the quantized linear system at a finite constant bit rate. Sufficiency of that dropout condition is proven by constructing appropriate quantization policies. Note that the obtained dropout condition does not require reliable dropout acknowledgments (ACKs). Moreover, this technical note derives a lower bound on the constant bit rates under which the quantized system is stabilizable. That bound is achievable when dropout ACKs are available. When dropout ACKs are not available, the bound can be achieved in some systems. Simulations are used to verify some of the analytical results.