Event‐Triggered Saturating Control for Synchronization of Lur'e Type Complex Dynamic Networks

ABSTRACT This article addresses the problem of synchronizing discrete‐time Lur'e type complex dynamic networks (CDNs) via dynamic event‐triggered control. In particular, it is considered that the control signal of each node is subject to input saturation. Using the Lyapunov Stability Theory, properties of slope‐restricted nonlinearities, and the linear matrix inequalities framework, constructive sufficient conditions are provided to ensure regional exponential synchronization of the CDN. Differently from other works in the current literature on CDNs, which require a trial‐and‐error procedure to select the event‐triggering mechanism (ETM) parameters, two systematic approaches, based on convex optimization, are presented to simultaneously synthesize (co‐design) the control law gains and the event‐generator parameters, aiming to reduce the number of events compared to a time‐triggered policy, with formal guarantees of regional synchronization with respect to a given admissible set of initial synchronization errors. Finally, a numerical example is presented to illustrate these approaches.