Synchronization of Coupled Multi-Agents via Non-Markovian Switching Topologies with Time-Varying Delays

This paper focuses on the synchronization of coupled multi-agents systems in complex networks with non-Markovian switching topologies and time-varying delays, which are formulated by a unified switching behavior combining a discrete adapted process and a Cox process. Based on the generalized Dynkin's formula, Doob's first convergence theorem and the generalized Halanay inequality, we establish the sufficient conditions for v-mean square synchronization and v-synchronization in probability with the construction of stochastic Lyapunov functional. Our research emphasizes non-Markovian, non-stationary, and non-ergodic cases. Additionally, the incorporation of time-varying delays contributes to more general results. And the theoretical results are validated through the numerical example.