Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces

✍ Scribed by Birgit Jacob, Hans J. Zwart (auth.)

• Publisher: Birkhäuser Basel
• Year: 2012
• Tongue: English
• Leaves: 221
• Series: Operator Theory: Advances and Applications 223
• Edition: 1
• Category: Library

✦ Synopsis

This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, then progresses smoothly to advanced topics in current research.

Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book is the first textbook on infinite-dimensional port-Hamiltonian systems. An abstract functional analytical approach is combined with the physical approach to Hamiltonian systems. This combined approach leads to easily verifiable conditions for well-posedness and stability.

The book is accessible to graduate engineers and mathematicians with a minimal background in functional analysis. Moreover, the theory is illustrated by many worked-out examples.

✦ Table of Contents

Front Matter....Pages i-xii
Introduction....Pages 1-12
State Space Representation....Pages 13-25
Controllability of Finite-Dimensional Systems....Pages 27-38
Stabilizability of Finite-Dimensional Systems....Pages 39-49
Strongly Continuous Semigroups....Pages 51-63
Contraction and Unitary Semigroups....Pages 65-77
Homogeneous Port-Hamiltonian Systems....Pages 79-96
Stability....Pages 97-109
Stability of Port-Hamiltonian Systems....Pages 111-122
Inhomogeneous Abstract Differential Equations and Stabilization....Pages 123-141
Boundary Control Systems....Pages 143-155
Transfer Functions....Pages 157-170
Well-posedness....Pages 171-196
Back Matter....Pages 197-217

✦ Subjects

Systems Theory, Control; Dynamical Systems and Ergodic Theory; Operator Theory; Partial Differential Equations