Pinning Synchronization Control of Complex Networks Under an Event‐Triggered Encoding Strategy

This paper addresses the pinning synchronization control problem for complex networks under an event‐triggered encoding mechanism. A sign‐based differential encoding‐decoding scheme incorporating an event‐triggered mechanism is proposed to encode the codeword into a one‐bit sign, thus saving limited network resources and enabling digital communication. The primary purpose of the considered problem is to design partial pinning controllers under the coding‐decoding scheme to achieve system synchronization and control cost savings. First, a lower bound of the inter‐event interval is enforced to exclude the Zeno behavior. Then, sufficient and necessary conditions on the bit rate of the communication channel are established to ensure the convergence of the proposed encoding‐decoding strategy. Subsequently, a selection strategy of controlled nodes based on the left Perron vector is proposed to guide controller placement. Moreover, by employing the input‐delay method, the original system is transformed into a model with bounded time‐varying delays. Sufficient conditions are derived to guarantee the exponential stability of the synchronization error, and explicit controller parameters are obtained in terms of the solution to a certain matrix inequality. Finally, a numerical simulation is given to validate the theoretical results.