Necessary and sufficient conditions for moment stability of positive Markov jump linear systems

This paper focuses on the problems of stability for positive Markov jump linear systems (PMJLSs) and its application to nonlinear Markov jump stochastic systems (MJSSs). First, we provide sufficient and necessary conditions for p-moment exponential stability of PMJLS. Then, based on the proposed results on p-moment exponential stability of PMJLS, we obtain explicit stability criteria for nonlinear MJSSs. Finally, two numerical examples are presented to confirm the validity of the obtained theoretical results.