The present paper proposes a control-theoretic approach to design rate-based controllers in order to flow-regulate the best-effort traffic through high-speed computer communication networks. Classical control theory and Schur-Cohn stability test are exploited to design the traffic controllers for high-speed networks. The stability of closed-loop congestion controlled systems is analysed by utilizing Schur-Cohn stability criterion, which leads to certain necessary and sufficient stability condition under which the controlled network is asymptotically stable in terms of buffer occupancy. The proposed stability condition is then shown to be a key tool in designing a wide scope of adaptive controllers. Simulations are performed that show good performance of such controlled networks.