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E-raamat: Linear Port-Hamiltonian Systems on Infinite-dimensional Spaces

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Linear Port-Hamiltonian Systems on Infinite-dimensional SpacesSuurem pilt
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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.

This introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems combines an abstract functional analytical approach with the physical approach to Hamiltonian systems. Offers many worked-out examples.

Arvustused

From the reviews:

This is an extremely well written monograph, which takes care to make the topic accessible to a vast audience of masters 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)

List of Figures
xi
1 Introduction
1(12)
1.1 Examples
1(5)
1.2 How to control a system?
6(4)
1.3 Exercises
10(2)
1.4 Notes and references
12(1)
2 State Space Representation
13(14)
2.1 State space models
13(6)
2.2 Solutions of the state space models
19(2)
2.3 Port-Hamiltonian systems
21(3)
2.4 Exercises
24(1)
2.5 Notes and references
25(2)
3 Controllability of Finite-Dimensional Systems
27(12)
3.1 Controllability
27(6)
3.2 Normal forms
33(3)
3.3 Exercises
36(2)
3.4 Notes and references
38(1)
4 Stabilizability of Finite-Dimensional Systems
39(12)
4.1 Stability and stabilizability
39(1)
4.2 The pole placement problem
40(4)
4.3 Characterization of stabilizability
44(3)
4.4 Stabilization of port-Hamiltonian systems
47(1)
4.5 Exercises
48(1)
4.6 Notes and references
49(2)
5 Strongly Continuous Semigroups
51(14)
5.1 Strongly continuous semigroups
51(6)
5.2 Infinitesimal generators
57(4)
5.3 Abstract differential equations
61(1)
5.4 Exercises
62(1)
5.5 Notes and references
63(2)
6 Contraction and Unitary Semigroups
65(14)
6.1 Contraction semigroups
65(8)
6.2 Groups and unitary groups
73(2)
6.3 Exercises
75(2)
6.4 Notes and references
77(2)
7 Homogeneous Port-Hamiltonian Systems
79(18)
7.1 Port-Hamiltonian systems
79(5)
7.2 Generation of contraction semigroups
84(8)
7.3 Technical lemmas
92(1)
7.4 Exercises
93(3)
7.5 Notes and references
96(1)
8 Stability
97(14)
8.1 Exponential stability
97(4)
8.2 Spectral projection and invariant subspaces
101(7)
8.3 Exercises
108(1)
8.4 Notes and references
109(2)
9 Stability of Port-Hamiltonian Systems
111(12)
9.1 Exponential stability of port-Hamiltonian systems
111(7)
9.2 An example
118(2)
9.3 Exercises
120(2)
9.4 Notes and references
122(1)
10 Inhomogeneous Abstract Differential Equations and Stabilization
123(20)
10.1 The abstract inhomogeneous Cauchy problem
123(7)
10.2 Outputs
130(2)
10.3 Bounded perturbations of C0-semigroups
132(1)
10.4 Exponential stabilizability
133(6)
10.5 Exercises
139(1)
10.6 Notes and references
140(3)
11 Boundary Control Systems
143(14)
11.1 Boundary control systems
143(4)
11.2 Outputs for boundary control systems
147(1)
11.3 Port-Hamiltonian systems as boundary control systems
148(6)
11.4 Exercises
154(1)
11.5 Notes and references
155(2)
12 Transfer Functions
157(14)
12.1 Basic definition and properties
158(5)
12.2 Transfer functions for port-Hamiltonian systems
163(4)
12.3 Exercises
167(2)
12.4 Notes and references
169(2)
13 Well-posedness
171(26)
13.1 Well-posedness for boundary control systems
171(10)
13.2 Well-posedness for port-Hamiltonian systems
181(5)
13.3 P1H diagonal
186(3)
13.4 Proof of Theorem 13.2.2
189(2)
13.5 Well-posedness of the vibrating string
191(2)
13.6 Exercises
193(2)
13.7 Notes and references
195(2)
A Integration and Hardy Spaces
197(12)
A.1 Integration theory
197(5)
A.2 The Hardy spaces
202(7)
Bibliography 209(6)
Index 215
Birgit Jacob received the M.Sc. degree in mathematics from the University of Dortmund in 1992 and the Ph.D. degree in mathematics from the University of Bremen in 1995. She held postdoctoral and professor positions at the universities of Twente, Leeds, Paderborn, at Berlin University of Technology and at Delft University of Technology. Since 2010, she has been with the University of Wuppertal, Germany, where she is a full professor in analysis. Her current research interests include the area of infinite-dimensional systems and operator theory, particularly well-posed linear systems and port-Hamiltonian systems.

Hans Zwart received his Master degree in 1984 and his Ph.D. degree in 1988, both in mathematics at the University of Groningen. Since 1988 he has been working at the Applied Mathematics Department, University of Twente, Enschede, The Netherlands. His research interests include analysis, controller design, and approximations of infinite-dimensional systems, in particular of port-Hamiltoninan systems.
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