Cluster Synchronization and Finite-Time Bounded for Complex Networks Under DoS Attacks and Encoding–Decoding Communication Protocol

In this paper, the finite-time (FNT) cluster synchronization of complex dynamic networks (CDNs) is discussed on the basis of encoding and decoding communication protocol involved in network attacks. Compared with general CDNs, the proposed discrete-time CDNs with denial-of-service (DoS) attacks and bit-rate constraints is considered, which is more consistent with the actual digital communication network. First, a complete encoding and decoding step based on the uniform quantizer is introduced. And more importantly, DoS attacks, whose duration and frequency duration are described by average dwell-time constraints, are considered in such steps, which clearly analyzes attacks influence on codeword string. In order to avoid encoding and decoding failure caused by unbounded encoding region, the attack is limited to a certain range, and the sufficient conditions for bounded encoding region are obtained. Second, in order to overcome the uncertainty of errors between encoded data and decoded data, sufficient conditions for decoding error convergence are obtained, which makes it possible to analyze the FNT cluster synchronization of CDNs based on the encoding decoding communication mechanism. Third, by Lyapunov stability theory, the synchronization controller is obtained to ensure that the nodes in the cluster are consistent, and the relationship between the upper bound of decoding error (UBDE) and the available bit rate is revealed. Finally, a simulation example shows that the bit-rate allocation protocol can reduce the UBDE and the time required for synchronization.