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E-raamat: Mathematics of Networks of Linear Systems

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  • Formaat: PDF+DRM
  • Sari: Universitext
  • Ilmumisaeg: 26-May-2015
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319166469
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Mathematics of Networks of Linear SystemsSuurem pilt
  • Formaat: PDF+DRM
  • Sari: Universitext
  • Ilmumisaeg: 26-May-2015
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319166469
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This book provides the mathematical foundations of networks of linear control systems, developed from an algebraic systems theory perspective. This includes a thorough treatment of questions of controllability, observability, realization theory, as well as feedback control and observer theory. The potential of networks for linear systems in controlling large-scale networks of interconnected dynamical systems could provide insight into a diversity of scientific and technological disciplines. The scope of the book is quite extensive, ranging from introductory material to advanced topics of current research, making it a suitable reference for graduate students and researchers in the field of networks of linear systems. Part I can be used as the basis for a first course in Algebraic System Theory, while Part II serves for a second, advanced, course on linear systems.

Finally, Part III, which is largely independent of the previous parts, is ideally suited for advanced research seminars aimed at preparing graduate students for independent research. “Mathematics of Networks of Linear Systems” contains a large number of exercises and examples throughout the text making it suitable for graduate courses in the area.

Arvustused

In the voluminous book under review the authors illustrate their perspective on modelling and control of networks of linear finite-dimensional systems. This is an excellent book that can be appreciated both by readers familiar with the polynomial approach, and by readers unaccustomed to functional models. The historical sections at the end of each chapter are helpful because they explain the broader context and suggest further reading to both types of readers. (Paolo Rapisarda, Mathematical Reviews, March, 2016)

1 Introduction
1(22)
1.1 Control of Parallel Connections
1(5)
1.2 Synchronization of Coupled Harmonic Oscillators
6(7)
1.3 Outline of the Book
13(10)
Part I Algebraic Systems Theory: Foundations
2 Rings and Modules of Polynomials
23(62)
2.1 Rings and Ideals
24(3)
2.2 Divisibility and Coprimeness of Polynomials
27(9)
2.3 Modules
36(4)
2.4 Minimal Basis of Modules of Polynomials
40(5)
2.5 Divisibility and Coprimeness of Polynomial Matrices
45(5)
2.6 Coprime Factorizations of Rational Matrix Functions
50(5)
2.7 Wiener--Hopf Factorizations
55(4)
2.8 Hermite and Smith Normal Forms
59(4)
2.9 Equivalence of Polynomial Matrices
63(2)
2.10 Structure Theorem and Quotient Modules
65(5)
2.11 Rings of Rational Functions
70(9)
2.12 Exercises
79(3)
2.13 Notes and References
82(3)
3 Functional Models and Shift Spaces
85(56)
3.1 Polynomial Models and the Shift Operator
86(5)
3.2 The Lattice of Shift-Invariant Subspaces
91(11)
3.3 Module Homomorphisms and Intertwining Maps
102(4)
3.4 Classification of Shift Operators
106(7)
3.5 Rational Models
113(9)
3.6 Duality
122(4)
3.7 The Matrix Chinese Remainder Theorem
126(2)
3.8 Toeplitz Operators
128(8)
3.9 Exercises
136(3)
3.10 Notes and References
139(2)
4 Linear Systems
141(68)
4.1 System Representations
142(9)
4.2 Reachability and Observability
151(3)
4.3 Abstract Realization Theory
154(7)
4.4 Equivalence of Realizations
161(3)
4.5 The Shift Realization
164(6)
4.6 Strict System Equivalence
170(8)
4.7 Poles and Zeros
178(10)
4.8 Open-Loop Control
188(13)
4.9 Exercises
201(3)
4.10 Notes and References
204(5)
Part II Algebraic Systems Theory: Advanced Topics
5 Tensor Products, Bezoutians, and Stability
209(72)
5.1 Tensor Products of Modules
211(13)
5.2 Tensored Polynomial and Rational Models
224(17)
5.3 Polynomial Sylvester Equation
241(3)
5.4 Generalized Bezoutians and Intertwining Maps
244(12)
5.5 Stability Characterizations
256(20)
5.6 Exercises
276(2)
5.7 Notes and References
278(3)
6 State Feedback and Output Injection
281(74)
6.1 State Feedback Equivalence
283(2)
6.2 Polynomial Characterizations
285(6)
6.3 Reachability Indices and the Brunovsky Form
291(13)
6.4 Pole Assignment
304(5)
6.5 Rosenbrock's Theorem
309(3)
6.6 Stabilizability
312(7)
6.7 Dynamic Output Feedback Stabilization
319(12)
6.8 Controlled Invariant Subspaces
331(10)
6.9 Conditioned Invariant Subspaces
341(6)
6.10 Zeros and Geometric Control
347(2)
6.11 Exercises
349(2)
6.12 Notes and References
351(4)
7 Observer Theory
355(56)
7.1 Classical State Observers
356(4)
7.2 Observation Properties
360(13)
7.3 Functional State Observers
373(11)
7.4 Existence of Observers
384(14)
7.5 Construction of Functional Observers
398(7)
7.6 Exercises
405(1)
7.7 Notes and References
406(5)
Part III Networks of Linear Systems
8 Nonnegative Matrices and Graph Theory
411(56)
8.1 Nonnegative Matrices and Contractions
412(5)
8.2 Perron--Frobenius Theorem
417(5)
8.3 Stochastic Matrices and Markov Chains
422(5)
8.4 Graphs and Matrices
427(7)
8.5 Graph Rigidity and Euclidean Distance Matrices
434(7)
8.6 Spectral Graph Theory
441(9)
8.7 Laplacians of Simple Graphs
450(7)
8.8 Compressions and Extensions of Laplacians
457(4)
8.9 Exercises
461(3)
8.10 Notes and References
464(3)
9 Interconnected Systems
467(40)
9.1 Interconnection Models
472(4)
9.2 Equivalence of Interconnected Systems
476(8)
9.3 Reachability and Observability of Networks of Systems
484(6)
9.4 Homogeneous Networks
490(2)
9.5 Special Coupling Structures
492(10)
9.6 Exercises
502(1)
9.7 Notes and References
503(4)
10 Control of Standard Interconnections
507(46)
10.1 Standard Interconnections
508(15)
10.2 Open-Loop Controls for Parallel Connections
523(19)
10.3 Open-Loop Control and Interpolation
542(7)
10.4 Exercises
549(2)
10.5 Notes and References
551(2)
11 Synchronization and Consensus
553(48)
11.1 Consensus and Clustering in Opinion Dynamics
554(12)
11.2 Synchronization of Linear Networks
566(9)
11.3 Synchronization of Homogeneous Networks
575(2)
11.4 Polynomial Model Approach to Synchronization
577(14)
11.5 Examples: Arrays of Oscillators
591(6)
11.6 Exercises
597(1)
11.7 Notes and References
598(3)
12 Control of Ensembles
601(44)
12.1 Control of Parametric Families of Systems
602(3)
12.2 Uniform Ensemble Reachability
605(12)
12.3 Control of Platoons
617(12)
12.4 Control of Partial Differential Equations
629(11)
12.5 Exercises
640(1)
12.6 Notes and References
641(4)
References 645(12)
Index 657
Paul A. Fuhrmann is Professor Emeritus in the Department of Mathematics at Ben-Gurion University of the Negev. His current research interests are in the following directions: Algebraic System Theory, control, observation and model reduction for networks of linear systems.





Uwe Helmke is Professor and Chair in Dynamical Systems and Control Theory at the University of Wuerzburg. His current research interests include Algebraic and Differential-Geometric Methods in Control, Linear Systems Theory, Optimization on Manifolds, Formation Control.
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