This paper proposes a new control problem of systems over asymmetric path-delay configurations on arbitrary communication networks, where the criterion is the H-infinity norm minimization via dynamic output-feedback controllers. Network-delay-dependent switching controllers are designed via a piecewise Lyapunov function approach as well as a common Lyapunov function approach. The controllers are found through convex optimization over linear matrix inequalities. (C) 2003 Elsevier Ltd. All rights reserved.