Parabolic matching of hyperbolic system using Control by Interconnection. Issue 1 (July 2017) - Trang Vu, N.M.; Trenchant, V.; Ramirez, H.; Lefèvre, L.; Le Gorrec, Y.
Abstract: The structural difference between one-dimensional (1D) hyperbolic and parabolic port Hamiltonian system (PHS) is discussed. Then, using a Control by Interconnection (CbI) approach, a distributed state feedback is designed in order to transform an hyperbolic PHS into a parabolic one, the latter being asymptotically stable and even purely dissipative (with no oscillating modes). Distributed wave damping in 1D vibro-acoustic pipes, using piezo actuators, is considered as an illustration example for the proposed control design.