Algebraic Invariance Conditions in the Study of Approximate (Null-)Controllability of Markov Switch Processes

TL;DR

This paper investigates algebraic invariance conditions that determine approximate null-controllability of Markov switch processes, providing computable criteria, necessary and sufficient conditions, and exploring their hierarchy and equivalence.

Contribution

It introduces new algebraic invariance criteria for controllability of Markov switch systems, including necessary and sufficient conditions and their hierarchical relationships.

Findings

Criteria are given in algebraic invariance terms.

Necessary and sufficient conditions are established.

Hierarchy of conditions is analyzed with counterexamples.

Abstract

We aim at studying approximate null-controllability properties of a particular class of piecewise linear Markov processes (Markovian switch systems). The criteria are given in terms of algebraic invariance and are easily computable. We propose several necessary conditions and a sufficient one. The hierarchy between these conditions is studied via suitable counterexamples. Equivalence criteria are given in abstract form for general dynamics and algebraic form for systems with constant coefficients or continuous switching. The problem is motivated by the study of lysis phenomena in biological organisms and price prediction on spike-driven commodities.