Asymptotic stability analysis of nonlinear stochastic semi-Markov jump systems

In this article, three different types of stochastic asymptotic stability for nonlinear stochastic semi-Markov jump systems (SSMJS) are investigated. Novel sufficient conditions for p$$ p $$th (p>0)$$ \left(p>0\right) $$-moment asymptotic stability, almost sure asymptotic stability and stochastic asymptotic stability in the large are obtained. It is remarkable that the obtained results in the latter case cover the results in existing literature. Finally, two examples are presented to confirm the validity of the obtained theoretical results.