Quantized Feedback Stabilizing Control for Multiple-input Networked Systems with Multiplicative Random Noises: a Stochastic Approach

The paper deals with the state feedback quadratic mean square stabilization problem for multiple-input discrete-time networked control systems with quantization errors and multiplicative random noises. An analytic solvability condition is first derived for the single-input case in terms of the Mahler measure of the system and the effective worst signal-to-noise ratio (EWSNR) of the channel. Moreover, relied on the technique of channel resource allocation, the result is further extended to the multiple-input case. Again, a sufficient solution is proposed by using the Mahler measure of the system and the overall EWSNR of the channels. It is observed from the current results that the solvability conditions derived from the robust control theory can be equivalently characterized by the EWSNR which is closely related to the information theory.