Mean square stabilization of multi-input systems over stochastic multiplicative channels

This paper deals with the mean square stabilization problem for multi-input networked systems via single packet or multiple packets transmission, where the unreliability of input channels is modeled by a multiplicative white noise. For the single packet case, the critical value (lower bound) of mean square capacity for ensuring mean square stabilization is given by adopting the bisection technique. For the m-parallel multiple packets transmission strategy, a necessary and sufficient condition on overall mean square capacity for mean square stabilization in terms of the Mahler measure or topological entropy of the plant is presented, under the assumption that the given network resource can be allocated among all the input channels. Applications in erasure-type channel and channel with stochastic sector-bounded uncertainty are provided to demonstrate the results.