Infinite-dimensional port-Hamiltonian systems: a system node approach

Abstract We consider an operator-theoretic approach to linear infinite-dimensional port-Hamiltonian systems. In particular, we use the theory of system nodes as reported by Staffans (Well-posed linear systems. Encyclopedia of mathematics and its applications, Cambridge University Press, Cambridge, UK, 2005) to formulate a suitable concept for port-Hamiltonian systems, which allows a unifying approach to systems with boundary as well as distributed control and observation. The concept presented in this article is further neither limited to parabolic nor hyperbolic systems, and it also covers partial differential equations on multi-dimensional spatial domains. Our presented theory is substantiated by means of several physical examples.