This paper aimed at investigating the exponential synchronization problem for a Markovian jump complex dynamical network through designing a state feedback controller. In this paper, it is supposed that both time delay and coefficient matrices switch between finite modes governed by a time-varying Markov process. The transition rate (TR) matrix of the Markov process is supposed to vary with time, and to be piecewise-constant. The time-varying transition rates are investigated under two cases: completely known TRs and partly unknown TRs, respectively. The synchronization problem of the proposed model is inspected by developing Lyapunov–Krasovski function with Markov-dependent Lyapunov matrices. The controller gain matrix for guaranteeing the synchronization problem is derived by using linear matrix inequalities. The resulted criteria depend on both delay size and the probability of the delay-taking value. Finally, a numerical example is provided to demonstrate the effectiveness of the theoretical results.

中文翻译：

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具有不确定跃迁率和模式相关耦合延迟的马尔可夫跳跃复杂动力网络的指数同步

本文旨在通过设计状态反馈控制器来研究马尔可夫跳跃复杂动态网络的指数同步问题。在本文中，假设时间延迟和系数矩阵在由时变马尔可夫过程控制的有限模式之间切换。马尔可夫过程的转移率 (TR) 矩阵应该随时间变化，并且是分段常数。在两种情况下研究了随时间变化的转换率：分别是完全已知的 TR 和部分未知的 TR。通过使用依赖于马尔可夫的 Lyapunov 矩阵开发 Lyapunov-Krasovski 函数来检查所提出模型的同步问题。用于保证同步问题的控制器增益矩阵是通过使用线性矩阵不等式导出的。结果标准取决于延迟大小和延迟获取值的概率。最后,通过数值例子证明了理论结果的有效性。