English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper considers the problem of stabilizing a discrete-time non-linearstochastic system over a finite capacity noiseless channel. Our focus is onsystems which decompose into a stable and unstable component, and the stabilitynotion considered is asymptotic ergodicity of the $\mathbb{R}^N$-valued stateprocess. We establish a necessary lower bound on channel capacity for theexistence of a coding and control policy which renders the closed-loop systemstochastically stable. In the literature, it has been established that undertechnical assumptions, the channel capacity must not be smaller than thelogarithm of the determinant of the system linearization, averaged over thenoise and ergodic state measures. In this paper, we establish that for systemswith a stable component, it suffices to consider only the unstable dimensions,providing a refinement on the general channel capacity bound for a large classof systems. The result is established using the notion of stabilizationentropy, a notion adapted from invariance entropy, used in the study ofnoise-free systems under information constraints.

Ergodicity of Controlled Stochastic Nonlinear Systems under Information Constraints: Refined Bounds via Splitting