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We analyze the stability of networks of passive systems with time delays in the interconnections. Building upon previous work where we complemented the passivity property with a “roll-off” integral quadratic constraint (IQC), here we expand our results to state space models. We first demonstrate how to verify that a state space model satisfies passivity and roll-off IQCs when the equilibrium is not known. We then illustrate the result on an Internet congestion control problem.