This paper deals with the problem of _∞ control for positive delay systems with semi-Markov process. The system is subjected to a semi-Markov process that is time-varying, dependent on the sojourn time, and related to Weibull distribution. The main motivation for this paper is that the practical systems such as the communication network model (CNM) described by positive semi-Markov jump systems (S-MJSs) always need to consider the sudden change in the operating process. To deal with the corresponding problem, some criteria about stochastic stability and _∞ boundedness are presented for the open-loop positive S-MJSs. Further, some necessary and sufficient conditions for state-feedback controller satisfying _∞ boundedness and positivity of the resulting closed-loop system is established in standard linear programming. Finally, the practical system about the CNM is given to verify the validity of the proposed method.

中文翻译：

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$\mathscr {L}_\infty$ 半马尔可夫过程的正时滞系统控制及其在通信网络模型中的应用


本文研究半马尔可夫过程正时滞系统的_∞控制问题。该系统服从半马尔可夫过程，该过程是时变的，取决于停留时间，并且与威布尔分布相关。本文的主要动机是，诸如正半马尔可夫跳跃系统（S-MJS）描述的通信网络模型（CNM）等实际系统总是需要考虑运行过程中的突然变化。为了解决相应的问题，对于开环正 S-MJS 提出了一些关于随机稳定性和 _∞ 有界性的准则。此外，在标准线性规划中建立了状态反馈控制器满足_∞有界性和所得到的闭环系统的正性的一些充分必要条件。最后给出了CNM的实际系统来验证所提方法的有效性。