In this paper, the problem of stability analysis and $L_1$-gain characterization for uncertain Markovian hybrid switching positive systems is investigated. The key feature in the paper is that the switching mechanism is described by a general class of hybrid switching laws, which is comprised of Markovian switchings and deterministic switchings. By using the mode-dependent time interval segmentation technique, multiple time-varying copositive Lyapunov functions are constructed. Then, the criteria ensuring the stochastically exponential stability and $L_1$-gain are derived. Finally, a numerical example and a practical one are provided to illustrate the obtained results.

中文翻译：

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稳定性分析和 ${升}_1$-不确定马尔可夫混合切换正系统的增益表征

在本文中，稳定性分析和问题 ${升}_1$研究了不确定马尔可夫混合切换正系统的增益特性。论文中的关键特征是切换机制由一类通用的混合切换定律描述，它由马尔可夫切换和确定性切换组成。通过使用依赖于模态的时间间隔分割技术，构造了多个时变协正李雅普诺夫函数。然后，确保随机指数稳定性的标准和${升}_1$- 增益是派生的。最后，给出了一个数值例子和一个实际例子来说明得到的结果。