Stationary and Ergodic Properties of Stochastic Non-Linear Systems Controlled over Communication Channels

摘要

This paper is concerned with the following problem: Given a stochasticnon-linear system controlled over a noisy channel, what is the largest class ofchannels for which there exist coding and control policies so that the closedloop system is stochastically stable? Stochastic stability notions consideredare stationarity, ergodicity or asymptotic mean stationarity. We do notrestrict the state space to be compact, for example systems considered can bedriven by unbounded noise. Necessary and sufficient conditions are obtained fora large class of systems and channels. A generalization of Bode's IntegralFormula for a large class of non-linear systems and information channels isobtained. The findings generalize existing results for linear systems.