The delay-dependent (D-D) stability problem is investigated for stochastic time-delay systems (STDSs) involving the Poisson process in this paper. Firstly, semi-martingale theory is conducted to tackle the jump information of Itô formula properly. Secondly, this paper studies the expectations of stochastic cross terms (SCTs) containing Poisson-type stochastic integrals (SIs), and proves that the expectation of the particular SCT is equal to the expectation of a Lebesgue integral. Thirdly, on the basis of the above results, this paper adopts the free weighting matrix (FWM) method to give a D-D stability condition by a linear matrix inequality (LMI). In the derivation, no bounding technique is used, and then the conservatism arising from the common bounding technique is avoided. Finally, an example is presented to show the effectiveness of the derived D-D stability condition.

研究了涉及泊松过程的随机时滞系统（STDSs）的时滞相关（DD）稳定性问题。首先，运用半-理论来正确处理伊藤公式的跳跃信息。其次，本文研究了包含Poisson型随机积分（SI）的随机交叉项（SCT）的期望，并证明了特定SCT的期望等于Lebesgue积分的期望。第三，在以上结果的基础上，本文采用自由加权矩阵（FWM）方法通过线性矩阵不等式（LMI）给出了DD的稳定性条件。在推导过程中，没有使用任何边界技术，因此避免了由于常见边界技术而产生的保守性。最后，