2 Port-Hamiltonian systems 2 . 1 From the Euler-Lagrange and Hamiltonian equations to port-Hamiltonian systems

It is shown how port-based modeling of lumped-parameter complex physical systems (multi-body systems, electrical circuits, electromechanical systems, ..) naturally leads to a geometrically defined class of systems, called port-Hamiltonian systems. The structural properties of these systems are discussed, in particular the existence of Casimir functions and their implications for stabilty. It is shown how a power-conserving interconnection of port-Hamiltonian systems defines another port-Hamiltonian system, and how this may be used for control by shaping the internal energy. Also implicit systems are incorporated in this framework. The link with H∞ control is established through the scattering representation. Extensions to the distributed-parameter case are briefly indicated.

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