Hamiltonian Systems as Passive Systems
In this chapter we deal with Euler-Lagrange and Hamiltonian systems as an important class of passive state space systems. First we consider the passivity of systems described by Euler-Lagrange equations, with an application to a tracking problem. We define the class of port-controlled Hamiltonian systems, including the examples of LC-circuits and mechanical systems with kinematic constraints. This framework is further extended to include dissipation. Stabilization procedures for port-controlled Hamiltonian systems, which exploit the Hamiltonian structure and the passivity property, are discussed. Finally, the notion of power-conserving interconnection is formalized, leading to the notion of implicit port-controlled Hamiltonian systems.
KeywordsHamiltonian System Kinematic Constraint Passive System Storage Function Dirac Structure
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