Synchronizing Markov jump discrete-time complex dynamical networks via periodic event-triggered controller

This paper focuses on guaranteed cost synchronization control for a class of Markov jump discrete-time complex dynamical networks (CDNs) with nonlinear node dynamics and time-varying delays. To dynamically capture the switched characteristics of real CDNs, the discrete time markov chain processes is given to model the dynamics of nodes in the network. The periodic event-triggered mechanism (ETM) is provided by comparing the last triggering state with the relative measurement error during periodic signal sampling by sensors. Different from existing continuous sampling methods, this method allows for expanding the interval between events and significantly reducing network energy consumption. Additionally, by constructing the discontinuous Lyapunov functionals and utilizing discrete-time Jensen’s inequality as well as Wirtinger’s inequality, a novel sufficient condition and corresponding controller for guaranteed cost synchronization control are derived for discrete-time CDNs considering communication delays. Finally, the theoretical results are validated with two numerical examples.