Almost sure stability of Markov jump linear systems with dwell-time constrained switching dynamics

The stability of a class of Markov jump linear systems (MJLS) characterized by constant transition rates and piecewise-constant system dynamics is investigated. For these Switching Dynamics Markov jump linear systems (SD-MJLS), almost sure exponential stability (ASE-stability) is analyzed by applying the ergodic law of large numbers under the assumption that suitable average contractivity conditions are satisfied. The main result is a sufficient condition that guarantees ASE-stability under constraints on the dwell-time between switching instants.