System Theoretical Properties of linear port-Hamiltonian Systems on Infinite-dimensional Spaces

Abstract

We consider a class of hyperbolic partial differential equations. This includes models of beams and waves as well as the transport equation and networks of nonhomogeneous transmission lines. We study infinite-dimensional linear port-Hamiltonian systems on a one-dimensional spatial domain with full boundary control and without internal damping and show that well-posed port-Hamiltonian systems are exactly controllable. Furthermore, we study the Riesz basis property of port-Hamiltonian systems. It is shown that the system operator is a discrete Riesz spectral operator if and only if it generates a strongly continuous group. Moreover, in this situation the spectrum consists of eigenvalues only, located in a strip parallel to the imaginary axis and they can decomposed into finitely many sets having each a uniform gap. In the last chapter equivalent conditions for contraction semigroup generation are derived for both infinite networks even of port-Hamiltonian systems of higher order and infinite-dimensional linear port-Hamiltonian systems of order one on the semi-axis.