Stabilization of continuous-time Markov/semi-Markov jump linear systems via finite data-rate feedback

TL;DR

This paper proposes a novel feedback control method for continuous-time Markov jump linear systems that ensures almost sure exponential stabilization under data-rate constraints, without requiring stabilizability of all modes.

Contribution

It introduces a sampling and quantization scheme with independent sampling and jump times, extending to semi-Markov systems and removing previous stabilizability assumptions.

Findings

Developed a numerically testable stabilization condition.

Extended results to semi-Markov jump linear systems.

Validated effectiveness through numerical examples.

Abstract

This paper investigates almost sure exponential stabilization of continuous-time Markov jump linear systems (MJLSs) under communication data-rate constraints by introducing sampling and quantization into the feedback control. Different from previous works, the sampling times and the jump times are independent of each other in this paper. The quantization is recursively adjusted on the sampling time, and its updating strategy does not depend on the switching in a sampling interval. In other words, the explicit value of the switching signal in a sampling interval is not necessary. The numerically testable condition is developed to ensure almost sure exponential stabilization of MJLSs under the proposed communication and control protocols. We also drop the assumption of stabilizability of all individual modes required in previous works about the switched systems. Moreover, we extend the result to the case of continuous-time semi-Markov jump linear systems (semi-MJLSs) via the semi-Markov kernel approach. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed communication and control protocols.