## Distributed-Parameter Port-Hamiltonian Systems

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CONTENTS-

1. Introduction
1.1. Motivating examples
1.2. Class of PDE’s
1.3. Dirac structures and port-Hamiltonian systems
1.4. Overview
1.5. Exercises

2. Homogeneous differential equation
2.1. Introduction
2.2. Semigroup and infinitesimal generator
2.3. Homogeneous solutions to the port-Hamiltonian system
2.4. Technical lemma’s
2.5. Properties of semigroups and their generators
2.6. Exercises
2.7. Notes and references

3. Boundary Control Systems
3.1. Inhomogeneous differential equations
3.2. Boundary control systems
3.3. Port-Hamiltonian systems as boundary control systems
3.4. Outputs
3.5. Some proofs
3.6. Exercises

4. Transfer Functions
4.1. Basic definition and properties
4.2. Transfer functions for port-Hamiltonian systems
4.3. Exercises
4.4. Notes and references

5. Well-posedness
5.1. Introduction
5.2. Well-posedness for port-Hamiltonian systems
5.3. The operator P1H is diagonal
5.4. Proof of Theorem 5.2.6.
5.5. Well-posedness of the vibrating string
5.6. Technical lemma’s
5.7. Exercises
5.8. Notes and references

6. Stability and Stabilizability
6.1. Introduction
6.2. Exponential stability of port-Hamiltonian systems
6.3. Examples
6.4. Exercises
6.5. Notes and references

7. Systems with Dissipation
7.1. Introduction
7.2. General class of system with dissipation
7.3. General result
7.4. Exercises
7.5. Notes and references

A. Mathematical Background
A.1. Complex analysis
A.2. Normed linear spaces
A.2.1. General theory
A.2.2. Hilbert spaces
A.3. Operators on normed linear spaces
A.3.1. General theory
A.3.2. Operators on Hilbert spaces
A.4. Spectral theory
A.4.1. General spectral theory
A.4.2. Spectral theory for compact normal operators
A.5. Integration and differentiation theory
A.5.1. Integration theory
A.5.2. Differentiation theory
A.6. Frequency-domain spaces
A.6.1. Laplace and Fourier transforms
A.6.2. Frequency-domain spaces
A.6.3. The Hardy spaces

Bibliography

Index