Equivalence between feedback systems with correlated multiplicative noisy channels and with additive noisy channels

摘要

In this work we study feedback control systems closed over noisy channels. We consider multiple inputs and multiple outputs, discrete time, linear and time-invariant feedback systems, and assume that the noisy channels are modeled by multiplicative noises with spatial correlation, or by additive noises with a constant gain. In this paper we explicitly determine conditions such that the first and second order moments of the stochastic processes of the system when the multiplicative channel is used, are equal to the corresponding moments obtained when the additive channel model is used. Such second order equivalence enable the use of a set of linear control tools for the analysis of feedback systems with correlated multiplicative channels.