In this article, the global fixed‐time synchronization issue is considered for semi‐Markovian switching discontinuous complex‐valued dynamical networks (CVDNs) with hybrid couplings and time‐varying delays, in which CVDNs are not divided into two real value systems, contrary to existing literature. First, a new fixed‐time convergence principle for complex‐valued nonlinear system with semi‐Markovian switching is developed. Second, to realize the fixed‐time synchronization, the state feedback controller with integral term and adaptive controller are designed, respectively. Under the complex‐valued differential inclusions framework, by utilizing Lyapunov‐Krasovskii functional method and inequality analysis technique, the global fixed‐time synchronization conditions are addressed in terms of linear matrix inequalities. Finally, two numerical simulations are given to illustrate the validity of the presented theoretical results.

中文翻译：

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具有半马尔可夫切换和混合耦合的不连续时滞复杂值网络的固定时间同步，通过自适应控制

在本文中，考虑了具有混合耦合和时变时滞的半马尔可夫切换不连续复数值动态网络（CVDN）的全局固定时间同步问题，其中CVDN不分为两个实数值系统，与之相反现有文献。首先，针对具有半马尔可夫切换的复数值非线性系统，开发了一种新的固定时间收敛原理。其次，为了实现定时同步，分别设计了带有积分项的状态反馈控制器和自适应控制器。在复值微分包含项框架下，利用Lyapunov-Krasovskii函数方法和不等式分析技术，利用线性矩阵不等式解决了全局固定时间同步条件。最后，