Intermittent synchronization for multi-link and multi-delayed large-scale systems with semi-Markov jump and its application of Chua’s circuits

Abstract

This paper focuses on exponential synchronization for multi-link and multi-delayed large-scale systems with semi-Markov jump (MLMDLSSMJ) via adaptive aperiodically intermittent control. It is challenging to overcome the impacts of multiple time delays and semi-Markov jump because of the intermittent property. The multi-delayed differential inequalities with semi-Markov jump are established to address this issue, which extend the existing Halanay-type differential inequalities. Several exponential synchronization criteria for intermittently controlled MLMDLSSMJ are built by using the inequality technique, Lyapunov method and graph theory. Notably, the exponential convergence rate is more accurate than the previous literature, which may aptly show the synchronization capability of MLMDLSSMJ. The exponential synchronization of Chua’s circuits network is investigated as a practical implementation of the theoretical results. Finally, to demonstrate the efficiency of the theoretical results, a few numerical simulations are provided.