The article proposes a kind of stability analysis method for nonlinear time-delayed semi-Markov jump systems with incremental quadratic constraints. To meet the requirement of stochastic stability, the sufficient conditions formulated by linear matrix inequalities are derived. Both the transition rate of semi-Markov process and the time delay are time-varying, which make the considered system more general than the systems governed by Markov process and whose time delay is invariant. The mode-dependent Lyapunov-Krasovskii function is employed to analyze the stability problem. Besides, incremental quadratic constraints are proposed to reduce the conservatism of sufficient conditions. Finally, the effectiveness and superiority of the proposed method is verified by an example of virus mutation treatment model.

提出了一种具有增量二次约束的非线性时滞半马尔可夫跳跃系统的稳定性分析方法。为满足随机稳定性的要求，推导出由线性矩阵不等式表示的充分条件。半马尔可夫过程的转移率和时延都是时变的，这使得所考虑的系统比由马尔可夫过程控制的时延不变的系统更通用。采用模态相关的Lyapunov-Krasovskii 函数来分析稳定性问题。此外，提出了增量二次约束以减少充分条件的保守性。最后，通过一个病毒变异处理模型实例验证了所提方法的有效性和优越性。