Conditions for Mean and First-Moment Stability of Positive Markov Jump Linear Systems with Time-Varying Subsystems

This work studies mean stability and first-moment stability of discrete-time positive Markov Jump Linear Systems with time-varying discrete modes. We adopt an approach based on linear co-positive Lyapunov functions that produces two sets of non-equivalent sufficient conditions with guaranteed exponential decay rates. Due to the general time-varying nature of the subsystems, the conditions require infinitely many tests. Hence, we show how one of the two introduced conditions can be finitely tested in the special case where the subsystems take uncertain values within polytopes.