The aim of this paper is to investigate exponential synchronization issue of time-varying multi-weights network with time delays (TMNTD) via periodic self-triggered intermittent sampled-data control. In particular, it is the first time to combine periodic self-triggered control and intermittent control with sampled-data, which has broader application prospects. Therein, self-triggered scheme is periodic judgment and aimed at intermittent control. And during control intervals in intermittent control, there is periodic sampled-data control. In addition, by applying tools of sampled-data control, intermittent control, event-driven control theory and stability analysis, some sufficient conditions are derived to guarantee exponential synchronization of TMNTD. After that, the theoretical results are utilized to research exponential synchronization issue of time-varying multi-weights Chua's circuits with time delays. Meantime, numerical simulations are provided to demonstrate the validity of the theoretical results. Finally, an image encryption algorithm is designed as a practical application of the developed results.
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