First-moment stability of Markov Jump Linear Systems with homogeneous and inhomogeneous transition probabilities

This work provides 1-moment stability conditions for discrete-time Markov Jump Linear Systems under time-homogeneous and time-inhomogeneous transition probabilities. For the latter, we further address the polytopic switching case. The analysis is carried out leveraging the comparison principle and the theory of positive systems, without nevertheless limiting the overall analysis to the latter. We provide sufficient stability conditions that only involve non-negative matrices and can be checked via linear programming.