Algebraic Theory for Multivariable Linear Systems

Name: Algebraic Theory for Multivariable Linear Systems
Brand: Academic Press
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BLOMBERG(Autor*in)

BLOMBERG(Herausgeber*in)

Academic Press

Erschienen am 14. Mai 2014

381 Seiten

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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

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