Finite Data-Rate Feedback Stabilization of Continuous-Time Switched Linear Systems with Unknown Switching Signal

TL;DR

This paper investigates the stabilization of continuous-time switched linear systems with limited feedback data, showing stabilizability under slow-switching conditions and proposing a practical coding scheme.

Contribution

It establishes conditions under which switched linear systems can be stabilized with finite data rate feedback, extending classical results to networked control scenarios.

Findings

Finite data rate feedback cannot stabilize arbitrary switching systems.

Slow-switching assumption enables stabilization with finite data rate.

Practical coder-controller effectively stabilizes systems under the proposed conditions.

Abstract

In this paper, we study the problem of stabilizing switched linear systems when only limited information about the state and the mode of the system is available, which occurs in many applications involving networked switched systems (such as cyber-physical systems, IoT, etc.). First, we show that switched linear systems with arbitrary switching, i.e., with no constraint on the switching signal, are in general not stabilizable with a finite data rate. Then, drawing on this result, we restrict our attention to systems satisfying a fairly mild slow-switching assumption, in the sense that the switching signal has an average dwell time bounded away from zero. We show that under this assumption, switched linear systems that are stabilizable in the classical sense remain stabilizable with a finite data rate. A practical coder-controller that stabilizes the system is presented and its applicability is demonstrated on numerical examples.