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System theoretical properties of linear port-Hamiltonian systems on infinite-dimensional spaces / vorgelegt von Julia Theresa Kaiser. Wuppertal, Februar 2021
Content
Introduction
Preliminaries
Preliminaries on evolution equations
Preliminaries on systems theory
Introduction to port-Hamiltonian systems
Class of port-Hamiltonian systems
Generation theorems
Boundary control and observation port-Hamiltonian systems
Spectrum of port-Hamiltonian systems withP1H() diagonal
Exact controllability of port-Hamiltonian systems
Sufficient condition for exact controllability
Closing remarks and open problems
Riesz bases of port-Hamiltonian systems
Preliminaries of bases
Toy examples
Discrete Riesz spectral operators
Discrete Riesz spectral port-Hamiltonian operators
Proof of the Main Result
Proof of the equivalence 2)3) of Theorem 5.3.3
Proof of the implication 2)1) of Theorem 5.3.3
Proof of the implication 1)2) of Theorem 5.3.3
Examples
Wave equation with boundary feedback
Timoshenko beam with boundary damping
Closing remarks and open problems
Generalization of port-Hamiltonian systems
Port-Hamiltonian systems in the infinite-dimensional setting
Examples for port-Hamiltonian systems in the infinite-dimensional setting
Port-Hamiltonian systems on the semi-axis
Examples for port-Hamiltonian systems on the semi-axis
Closing remarks and open problems
Bibliography
Acknowledgement