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At present, the study of the finite-dimensional stability of interconnected systems has been carried out extensive research and has been made many meaningful conclusions, but infinite-dimensional concept of the stability of interconnected systems didnt be introduced until 1971 by Chu in the paper [1] when considering the vehicle-following system.Chu defined the stability about vehicle-following system.Recently, Swaroop and Hedrick [4-5] introduced a kind of Lyapunov stability for hierarchical infinite interconnected systems.The stability analysis of hierarchical infinite interconnected systems was studied by Socha and Popp[3] for linear systems and by Mao[2] for nonlinear systems.