First-moment stability conditions for continuous-time Markov Jump Linear Systems with stationary and time-varying transition rates

This work deals with 1-moment stability for continuous-time Markov Jump Linear Systems under stationary and time-varying transition rates. The analysis leverages comparison systems to exploit stability results from the context of positive systems. For the case of stationary transition rates, we introduce novel sufficient conditions of 1 -moment stability that only involve Metzler matrices and can be thus checked via linear programming. Such conditions offer a computationally simpler and less restrictive stability characterization with respect to mean square stability. For the general case of timevarying transition rates, a novel approach that leverages recent results on positive time-varying systems is adopted, providing 1 moment stability conditions given in form of linear inequalities, albeit infinite-many in the general case. The theoretical findings are illustrated by means of numerical examples.