On Component-wise Asymptotic Moment Stability of Continuous-time Markov Jump Linear Systems

In addition to the known stochastic stability properties of asymptotic moment stability and almost sure global asymptotic stability for continous-time Markov jump linear systems, in this work, we propose component-wise asymptotic moment stability and study the relations between these stochastic stability properties. Next, we show that the component-wise 1st and 2nd moments of a Markov jump linear system can be precisely computed by solving linear ordinary differential equations. Consequently, necessary and sufficient conditions for component-wise asymptotic 1st and 2 nd moment stability are obtained. Lastly, we test stochastic stability of several numerical examples via our criteria, one of which consists of all unstable flow and all unstable jumps, yet has all the stochastic stability properties aforementioned.