Robustness of critical bit rates for practical stabilization of networked control systems

TL;DR

This paper investigates how the minimum data rate needed for stabilizing networked control systems remains stable under small system changes, using invariance entropy for deterministic nonlinear systems.

Contribution

It proves the continuity of invariance entropy under certain conditions, demonstrating the robustness of critical bit rates for practical stabilization.

Findings

Invariance entropy varies continuously with system parameters.

Critical bit rate is robust to small perturbations.

Provides theoretical foundation for stable digital control over networks.

Abstract

In this paper we address the question of robustness of critical bit rates for the stabilization of networked control systems over digital communication channels. For a deterministic nonlinear system, the smallest bit rate above which practical stabilization (in the sense of set-invariance) can be achieved is measured by the invariance entropy of the system. Under the assumptions of chain controllability and a uniformly hyperbolic structure on the set of interest, we prove that the invariance entropy varies continuously with respect to system parameters. Hence, in this case the critical bit rate is robust with respect to small perturbations.