This paper presents a design method of decentralized systems with informational connection. The informational connection in this paper denotes a event link which establish a signal links among physical controlled plants via communication network. A dynamic transition of informational connection among decentralized systems is considered and the mathematical structures are discussed using a concept of eigenvalues and eigen-connections over the Galois field GF (2). The global system has variable structure characteristics due to the transition of informational connection. Examples of decentralized variable structure systems are shown. In an industry field, there are many engineering systems that have dynamic transition of informational connection. The mathematical model would be useful for analysis and synthesis of various informationally connected systems.