In this paper, we consider dynamical models of computer networks and derive a synthesis method for stabilizing congestion controllers. Moreover we verify the efficacy of the designed stabilizing congestion controllers using our developed network testbed. First we show dynamical models of TCP/AQM (transmission control protocol/active queue management) networks. The dynamical models of TCP/AQM networks consists of models of TCP window size, queue length and AQM mechanisms. Second we propose to describe the dynamical models of TCP/AQM networks as linear systems with self-scheduling parameters, which also depend on information delay. Here we focus on the constraints on the maximum queue length and TCP window-size, which are the network resources in TCP/AQM networks. Linear system with a self-scheduling parameter and an information delay are derived for dynamical models of TCP/AQM networks. We show a design method of memoryless state feedback controllers for derived linear system with a self-scheduling parameter and an information delay. Finally the effectiveness of the proposed method is evaluated by using ns-2 (Network Simulator Ver.2) simulator and our developed network testbed.