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

2015/06/12 by Serdar Yüksel, Yüksel, Serdar
Computer Science · Engineering · #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Petri Nets in System Modeling #Probability (math.PR) #Stability and Control of Uncertain Systems

paper · pdf · doi:10.48550/arxiv.1506.04013

openalex publication_date 2015/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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