Read more
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.
List of contents
1 Introduction.- 2 State Space Representation.-3 Controllability of Finite-Dimensional Systems.- 4 Stabilizability of Finite-Dimensional Systems.- 5 Strongly Continuous Semigroups.- 6 Contraction and Unitary Semigroups.- 7 Homogeneous Port-Hamiltonian Systems.- 8 Stability.- 9 Stability of Port-Hamiltonian Systems.- 10 Inhomogeneous Abstract Differential Equations and Stabilization.- 11 Boundary Control Systems.- 12 Transfer Functions.- 13 Well-posedness.- A Integration and Hardy spaces.- Bibliography.- Index.
Additional text
From the reviews:
“This is an extremely well written monograph, which takes care to make the topic accessible to a vast audience of master’s students and also beginning Ph.D. students, as well as researchers who want an introduction to the topic of the mathematical theory of the control of systems of evolution equations. … provide an insight into some fundamental definitions and results through a concise tutorial which focuses on linear systems of evolution equations, their systems properties and their relation with the dynamical models of physical systems.” (Bernhard M. Maschke, Mathematical Reviews, August, 2013)
Report
From the reviews:
"This is an extremely well written monograph, which takes care to make the topic accessible to a vast audience of master's students and also beginning Ph.D. students, as well as researchers who want an introduction to the topic of the mathematical theory of the control of systems of evolution equations. ... provide an insight into some fundamental definitions and results through a concise tutorial which focuses on linear systems of evolution equations, their systems properties and their relation with the dynamical models of physical systems." (Bernhard M. Maschke, Mathematical Reviews, August, 2013)
