Decay rates for stabilization of linear continuous-time systems with random switching

TL;DR

This paper demonstrates that for certain linear switched systems, controllability guarantees almost sure stabilization with any desired exponential decay rate using state feedback, leveraging the Multiplicative Ergodic Theorem.

Contribution

It establishes a controllability-based criterion for almost sure stabilization with arbitrary decay rates in continuous-time linear switched systems.

Findings

Almost sure stabilization achieved for controllable systems

Arbitrary exponential decay rates are possible with state feedback

Utilizes the Multiplicative Ergodic Theorem in the analysis

Abstract

For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative Ergodic Theorem applied to an associated system in discrete time. This result is related to the stabilizability problem for linear persistently excited systems.