This paper is concerned with the global stability for a general discrete-time coupled system on network (DTCSN). A systematic method of constructing global Lyapunov function for the DTCSN is provided by combining graph theory and the Lyapunov method. Consequently, some novel global stability principles, which have close relation to the topology property of the network, are given. They have important leading significance in the design and applications for the globally stable DTCSNs. In addition, to present the effectiveness and applicability of the results, the proposed theory is used to analyze the global stability for some practical models and numerical methods.
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