This work is concerned with the problem of reachable set estimation for a class of singular semi-Markov jump system with time-varying delay under zero initial condition. Firstly, the technique of linear matrix inequality and two different methods are used to deal with the uncertain transition rate. Secondly, the boundary technique is applied to the fast subsystem without any assumptions about the system matrix. Finally, the reachable set mean-square bounded conditions for singular semi-Markov jump system with time-varying delay are given. The numerical simulation verifies the correctness of the theoretical analysis.

中文翻译：

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奇异半马尔可夫跳跃系统的可达集估计

本文研究的是一类零初始条件下时变时滞奇异半马尔可夫跳跃系统的可达集估计问题。首先，利用线性矩阵不等式技术和两种不同的方法来处理不确定的转移率。其次，边界技术应用于快速子系统，而不对系统矩阵做任何假设。最后，给出了时变时滞奇异半马尔可夫跳跃系统的可达集均方有界条件。数值模拟验证了理论分析的正确性。