Introduction to Algebraic System Theory

Name: Introduction to Algebraic System Theory
Brand: Academic Press
Price: 61.95 EUR
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Academic Press

Erschienen am 14. Mai 2014

363 Seiten

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978-0-08-095659-6 (ISBN)

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Front Cover
Introduction to Algebraic System Theory
Copyright Page
CONTENTS
Preface
CHAPTER 1. INTUITIONS
1.1 Misconceptions
1.2 An Aspect of Algebra
1.3 An Aspect of System Theory
1.4 An Aspect of Algebraic System Theory
1.5 A Glimpse of Negative Feedback
1.6 Discussion
CHAPTER 2. SET-DYNAMICAL SYSTEMS
2.1 Sets, Functions
2.2 Local Dynamical Functions
2.3 Relations
2.4 Definition of a Set-Dynamical System
2.5 Order Reduction
2.6 The Key Triangle
2.7 Signal Set Equivalences
2.8 Local Dynamical Equivalences
2.9 Induced Set-Dynanical Systems
2.10 Example
2.11 Discussion
CHAPTER 3. OBSERVERS AND REGULATION
3.1 Posets
3.2 Lattices
3.3 Global Dynamical Functions
3.4 Reachability
3.5 Observability
3.6 The Relational Lattice
3.7 The Equivalence Lattice
3.8 Observer Models
3.9 Regulator Problem Formulation
3.10 The Internal Model Principle
3.11 Discussion
CHAPTER 4. GROUP MORPHIC SYSTEMS
4.1 Groups and Morphisms
4.2 The SDS with Group Structure
4.3 Interconnected GRMPSs: Series
4.4 Interconnected GRMPSs: Parallel
4.5 Refining the Triangle
4.6 GRMPSs: Finite Transition
4.7 Reachability Revisited
4.8 Observability Revisited
4.9 The State Group
4.10 Discussion
CHAPTER 5. INVERSES OF GROUP MORPHIC SYSTEMS
5.1 Rings
5.2 GRMP Global Output Calculations
5.3 State Feedback Interconnection
5.4 Feedback and the Reachable Subgroup
5.5 Invertibility with Delay L
5.6 Inverse GRMP Systems
5.7 Example
5.8 Decoupling with State Measurement
5.9 Discussion
CHAPTER 6. INTERCONNECTED SYSTEMS
6.1 Key Triangle Revisited
6.2 Notions of Interconnection
6.3 Identical Systems: Series, Parallel, Interplays
6.4 Identical Systems: The Ring Structure
6.5 Extension
6.6 A Description Simplification for Systems
6.7 The Ring of Compatible Systems
6.8 The Ring of Simplified Systems
6.9 Quotients on Interconnected Systems
6.10 Discussion
CHAPTER 7. ASPECTS OF MODULE MORPHIC SYSTEMS
7.1 Modules
7.2 Signal Representation
7.3 Module Morphic Systems
7.4 Matrix Module Morphic Systems
7.5 Commutative Rings and Special Modules
7.6 The Transfer Function: A Simple Case
7.7 Transfer Functions and Impulse Response
7.8 The Key Triangle-One More Time
7.9 Remarks on Realization Theory
7.10 Discussion
REFERENCES AND FURTHER READING
Index

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