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

TL;DR

This paper investigates the conditions under which stochastic non-linear systems controlled over noisy communication channels can achieve stability properties like stationarity and ergodicity, extending classical linear system results to more general non-linear cases.

Contribution

It provides necessary and sufficient conditions for stability of non-linear systems over communication channels, generalizing Bode's Integral Formula beyond linear systems.

Findings

Derived conditions for stochastic stability over noisy channels

Generalized Bode's Integral Formula for non-linear systems

Extended stability analysis to unbounded noise systems

Abstract

This paper is concerned with the following problem: Given a stochastic non-linear system controlled over a noisy channel, what is the largest class of channels for which there exist coding and control policies so that the closed loop system is stochastically stable? Stochastic stability notions considered are stationarity, ergodicity or asymptotic mean stationarity. We do not restrict the state space to be compact, for example systems considered can be driven by unbounded noise. Necessary and sufficient conditions are obtained for a large class of systems and channels. A generalization of Bode's Integral Formula for a large class of non-linear systems and information channels is obtained. The findings generalize existing results for linear systems.