Stability and disturbance attenuation for a switched Markov jump linear system

TL;DR

This paper develops conditions for the stability and disturbance attenuation of a class of Markov jump linear systems with unknown transition probabilities, using linear matrix inequalities for efficient computation.

Contribution

It provides necessary and sufficient conditions for stability and disturbance attenuation in time-inhomogeneous Markov jump systems with unknown transition probabilities.

Findings

Conditions expressed as linear matrix inequalities

Efficient solvability of stability criteria

Applicable to systems with unknown transition dynamics

Abstract

We address a class of Markov jump linear systems that are characterized by the underlying Markov process being time-inhomogeneous with a priori unknown transition probabilities. Necessary and sufficient conditions for uniform stochastic stability and uniform stochastic disturbance attenuation are reported. In both cases, conditions are expressed as a set of finite-dimensional linear matrix inequalities that can be solved efficiently.