This paper presents an expression of system connection considering transmission delay. In a research field of decentralized system or information system, expression method of the system connection is very important issue. Therefore some expression methods of system connection have been proposed so far. However those expressions are mainly based on binary operation and can not consider the transmission delay on connection paths although the concept of time is efficient for expression of system connection. In this paper, expression methods of system connection considering transmission delays on the paths are proposed. Those expressions are based on exponential-type expression and can express both connections and transmission delays. Furthermore the expression that can express connections, transmission delays and past subsystems is also proposed. As one example of the application of proposed expressions, application for path selection of the design of network-based control system is described.
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