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In this paper, an analytical method for a design of a congestion control scheme in packet switching network is presented .This scheme is particularly suitable for implementation in ATM Switch Systems, for the support of the available bit rate (ABR) service in ATM networks .The control method is rate based with a local feedback controller associated with each switch node. The controller is a generalization of the standard proportional-plus- derivative controller, with the difference that extra higher - order derivative terms are involved to accommodate for delay in networks. It is shown that there exist a set of control gain that result in applying asymptotic stability of the linearized network model . The use of adaptive control for finding the state feedback gains for asymptotically stability is our main purposes. Since the proposed approach considers the case of multiple congested nodes, it stabilizes the entire links in the network.