Mean square detectability of multi-output systems over stochastic multiplicative channels

This study addresses the mean square detectability problem for multi-output networked systems via single packet or multiple packets transmission, where a multiplicative white noise model the unreliability of output channels. For the single packet case, by adopting the bisection technique, the authors give the critical value (lower bound) of mean square capacity for ensuring mean square detectability. For the m-parallel multiple packets transmission strategy, a necessary and sufficient condition on overall mean square capacity for mean square detectability 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 output channels. Applications in erasure-type channel and channel with stochastic sector-bounded uncertainty are provided to demonstrate the results.