Algebraic Theory for Multivariable Linear Systems
Published on 14. May 2014
381 pages
978-0-08-095672-5 (ISBN)
Description
Algebraic Theory for Multivariable Linear Systems
More details
Series
Language
English
Place of publication
Oxford
United Kingdom
ISBN-13
978-0-08-095672-5 (9780080956725)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Hans Blomberg | Raimo Ylinen
Algebraic Theory for Multivariable Linear Systems
Book
01/1983
Academic Press
€72.43
Article exhausted; check different version
Content
- Front Cover
- Algebraic Theory for Multivariable Linear Systems
- Copyright Page
- Contents
- Preface
- Acknowledgements
- List of Symbols
- Chapter 1. Introduction
- 1.1 Differential input-output relations and systems
- 1.2 Compositions of differential input-output relations
- 1.3 Algebraic foundations
- 1.4 Properties of differential input-output relations
- 1.5 Feedback compensation and control
- 1.6 Concluding remarks
- Part I: Basic Concepts of Systems Theory
- Chapter 2. Systems and system descriptions
- 2.1 Parametric input-output mappings. Abstract input-output systems. System descriptions
- 2.2 Time systems. Dynamic systems
- 2.3 Linear systems
- Chapter 3. Interconnections of system
- 3.1 Formal definition of an interconnection of a family of systems
- 3.2 Input-output relations determined by an interconnection of a family of systems
- 3.3 Determinateness with respect to the empty set of realizability conditions
- 3.4 Determinateness with respect to a general set of realizability conditions
- 3.5 Illustrative example
- Part II: Differential Systems. The Module Structure
- Chapter 4. Generation of differential systems
- 4.1 Signal spaces and differential operators
- 4.2 Matrix differential equations
- Chapter 5. The C[p]-module x
- 5.1 Suitable signal spaces x
- 5.2 The ring C [p] of polynomial operators. The C[p]-module x
- 5.3 Relationship between polynomial matrix operators and matrices over C[p]
- 5.4 Fundamental properties of polynomial matrix operators
- Chapter 6. Differential input-output relations. Generators
- 6.1 Introduction. Regular differential input-output relations and regular generators
- 6.2 Input-output equivalence. Complete invariants and canonical forms for input-output equivalence
- 6.3 The transfer matrix. Proper and strictly proper transfer matrices, generators, and differential input-output relations
- 6.4 Transfer equivalence. Complete invariants and canonical forms for transfer equivalence. Controllability
- 6.5 Proofs of theorems (6.2.1), (6.2.2) and (6.4.8)
- 6.6 Comments on canonical forms. Canonical row proper forms
- Chapter 7. Analysis and synthesis problems
- 7.1 An elimination procedure
- 7.2 Compositions and decompositions of regular differential input-output relations. Observability
- 7.3 A parallel composition
- 7.4 Parallel decompositions of regular differential input-output relations
- 7.5 Illustrative example
- 7.6 A series composition
- 7.7 Series and series-parallel decompositions of regular differential input-output relations
- 7.8 The Rosenbrock representation
- 7.9 The state-space representation
- 7.10 The Rosenbrock representation and the state-space representation as decompositions of regular differential input-output relations. Equivalence relations
- 7.11 Observer synthesis problem
- 7.12 Feedback compensator synthesis
- Part III: Differential Systems. The Vector Space Structure
- Chapter 8. The projection method
- 8.1 Reason for choosing a space of generalized functions as signal space
- 8.2 The basic signal space D of generalized functions. Projection mappings. Subspaces of D Generalized causality
- 8.3 The vector space x over C(p)
- 8.4 Compositions of projections and differential operators. Initial condition mappings
- 8.5 The projection method
- Chapter 9. Interconnections of differential systems
- 9.1 Two interconnections
- 9.2 Systems associated with compositions of input-output relations
- 9.3 The main results
- 9.4 Illustrative example
- Part IV: Difference Systems
- Chapter 10. Generation of difference systems
- 10.1 Signal spaces and shift operators
- 10.2 Matrix difference equations
- Chapter 11. The module structure
- 11.1 Suitable signal spaces
- 11.2 The rings C[r], C(r], C[1/r] and C(r) and modules over them
- 11.3 Polynomial and rational matrix operators and polynomial and rational matrices
- Chapter 12. Difference input-output relations. Generators
- 12.1 Regular difference input-output relations and regular generators
- 12.2 Input-output equivalence. Canonical forms for input-output equivalence. Causality
- 12.3 The transfer matrix. Properness and causality
- 12.4 Transfer equivalence. Canonical forms for transfer equivalence Controllability.
- Chapter 13. Analysis and synthesis problems
- 13.1 Compositions and decompositions of regular difference input-output relations. Observability
- 13.2 The feedback composition
- Chapter 14. The vector space structure. The projection method
- 14.1 Signal space
- 14.2 The modules and vector spaces of quotients
- 14.3 Compositions of projections and delay operators. Initial condition mappings
- 14.4 The projection method
- Appendices
- A1 Fundamentals of abstract algebra
- A2 Polynomials and polynomial matrices
- A3 Polynomials and rational forms in an endomorphism
- A 4 The space D of generalized functions
- References
- Index
