Mean Stability of Positive Markov Jump Linear Systems With Homogeneous and Switching Transition Probabilities

This brief investigates the mean stability problem of positive Markov jump linear systems (PMJLSs) in the discrete- time domain. First, some sufficient and necessary conditions are presented for PMJLSs with homogeneous transition probability (TP) by analyzing the time evolution of the first-order moment of the state. Then, by using a copositive Lyapunov function approach, a computable sufficient condition for the PMJLSs with switching TPs is proposed in the framework of dwell time to guarantee the mean stability. Finally, some numerical examples are given to demonstrate the effectiveness of the obtained theoretical results.