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DOI: 10.23952/cot.2026.36
Received November 30, 2024; Accepted July 29, 2025; Published online April 22, 2026
Abstract. This paper considers the problem of stabilizing a discrete-time non-linear stochastic dynamical system over a finite capacity noiseless channel. Asymptotic ergodicity of the state process is the stability notion considered. In this article, we first provide a review of recent results on the subject, and note that in the literature it has been established that under technical assumptions, the channel capacity must not be smaller than the logarithm of the determinant of the linearized system, averaged over the noise and ergodic state measures. In this paper, we establish that for systems with a stable subspace, it suffices to integrate over only the unstable dimensions, providing a refinement on the general data-rate bound for a large class of systems. The result is established using the notion of stabilization entropy, a notion adapted from invariance entropy, used in the study of noise-free systems under information constraints. This analysis and the associated refined bounds highlight the utility of a stochastic geometric approach when compared with information theoretic methods. A detailed comparison and reflection on these two approaches is also presented in the paper.
How to Cite this Article:
N. García, C. Kawan, S. Yüksel, Ergodic stabilization of controlled stochastic nonlinear systems under information constraints: Geometric analysis with stable and unstable coordinate splitting, Commun. Optim. Theory 2026 (2026) 36.