Event-triggered [formula omitted] control for partial unknown Markov jump discrete-time complex networks with distributed delay

Abstract

Periodic event triggering, an important control mechanism, effectively saves communication resources and energy, making it highly valuable in networked control systems. This study focuses on the comprehensive utilization of periodic sampling pattern and event triggering mechanism to achieve synchronization control of a class of discrete-time Markov jump complex dynamic networks (CDNs) with H∞ performance index. Firstly, a comprehensive CDNs model is established incorporating Markovian jump parameters with incomplete transition probabilities, time-varying delays, and external random disturbances, making it more readily implementable in practical engineering scenarios. Secondly, a novel periodic event-triggered control strategy is proposed. In this strategy, the threshold parameters and weighting matrix in the event-triggering condition are mode-dependent, which can achieve better resource efficiency and effectively avoid the Zeno phenomenon. Thirdly, a discontinuous Lyapunov–Krasovskii functional is designed to capture information about discrete periodic sampling patterns. By applying free-weighting matrix, Jensen’s inequality, and Wirtinger’s inequality, sufficient conditions and controller for CDNs synchronization are derived with lower conservativeness. Finally, a simulation example is provided to demonstrate the feasibility and effectiveness of the theoretical results obtained.