System Theory -- A Modern Approach, Volume 1

Name: System Theory -- A Modern Approach, Volume 1 | Linear Ordinary and Functional Differential Equations
Brand: Jossey-Bass
Price: 142.99 EUR
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Linear Ordinary and Functional Differential Equations

Henri Bourlès(Autor*in)

Jossey-Bass (Verlag)

1. Auflage

Erschienen am 16. Mai 2024

320 Seiten

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978-1-394-29754-2 (ISBN)

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Inhalt

Cover
Title Page
Copyright Page
Contents
Preface
List of Notations
Chapter 1 Representation of Systems: A Historical Overview
1.1. Transfer functions and matrices
1.1.1. Transfer functions
1.1.2. Transfer matrices
1.1.3. The discrete-time case
1.2. State-space representation
1.2.1. Continuous-time state-space systems
1.2.2. Discrete-time state-space systems
1.2.3. Controllability and observability
1.2.4. Poles of a state-space system
1.2.5. Stability of linear time-invariant systems
1.3. "Geometric" approach
1.3.1. Formalism of the geometric approach
1.3.2. Reachable and non-observable subspaces
1.3.3. State-feedback controls, observers
1.3.4. Canonical Kalman decomposition, stabilizability and detectability
1.4. Polynomial matrix description
1.4.1. PBH test (Hautus criterion)
1.4.2. Rosenbrock representation
1.5. The behavioral approach
1.5.1. Controllability without control variables
1.5.2. Observability in the behavioral approach
1.6. Module of a system
1.6.1. Using modules in control theory
1.6.2. The Fliessian approach
1.6.3. Characterization in terms of modules of controllability and observability
1.7. The formalism of algebraic analysis
1.7.1. Nature of algebraic analysis
1.7.2. Oberst's contribution and its consequences
Chapter 2 Linear Systems: Concepts and General Results
2.1. Control systems
2.1.1. The formalism of control systems
2.1.2. Transfer matrix: general case
2.1.3. State-space representation of a control system
2.2. Strict equivalence of Rosenbrock systems
2.2.1. Admissible Rosenbrock representations
2.2.2. Strict equivalence
2.3. Controllability, observability and their duality: the algebraic point of view
2.3.1. Algebraic controllability
2.3.2. Algebraic controllability of state-space systems (continuous time)
2.3.3. Algebraic controllability of state-space systems (discrete-time)
2.3.4. Algebraic duality
2.3.5. Algebraic observability and the algebraic duality principle
2.4. Reachability, observability and their duality: Kalmanian point of view
2.4.1. Complete controllability of a state-space system (continuous time)
2.4.2. Complete reachability and controllability of a state-space system (discrete-time)
2.4.3. Observability of state-space systems (continuous-time)
2.4.4. Complete observability and constructibility of state-space systems (discrete-time)
Chapter 3 Poles and Zeros of Linear Systems, Interconnectedness and Stabilization
3.1. Poles and zeros of continuous or discrete invariant linear systems
3.1.1. System poles, transmission poles and zeros
3.1.2. Input-output-decoupling zeros and hidden modes
3.1.3. Relations between poles, transmission poles and hidden modes
3.1.4. Invariant zeros
3.1.5. Dynamic interpretation of different poles and zeros
3.2. Poles and zeros of interconnected systems
3.2.1. Diagram of a control system
3.2.2. System interconnection
3.2.3. Series interconnection
3.2.4. Parallel interconnection
3.2.5. Feedback interconnection
3.2.6. Youla-Kucera parametrization of stabilizing controllers
Chapter 4 Systems with Differential Equations and Difference Equations
4.1. Systems governed by functional differential equations
4.1.1. Functional differential equation of retarded type
4.1.2. Functional differential equations of neutral type
4.1.3. Case of infinite delays
4.1.4. Linear functional differential equations
4.1.5. Stability of functional differential equations
4.2. Time-invariant linear systems with lumped delays
4.2.1. Definition and simplified framing
4.2.2. Commensurability or incommensurability of delays
4.2.3. Case of commensurable delays
4.2.4. Homological questions
4.3. Time-invariant linear systems with distributed delays
4.3.1. Ring H: case of non-commensurable delays
4.3.2. Rings H and H0: case of commensurable delays
4.3.3. Controllability and observability of H-systems
4.3.4. Stability of H-systems
4.3.5. Poles and zeros of H-systems
Appendix The Mathematics of the Theory of Systems
A.1. Laplace transform
A.1.1. Laplace transform of functions
A.1.2. Laplace transform of distributions having at most exponential growth
A.1.3. Laplace transform of any distributions and ultradistributions
A.2. C0-semi-groups of operators
A.2.1. Bounded, compact or closed operators and their resolvent
A.2.2. Exponential of a bounded operator and its relation with there solvent
A.2.3. Resolvent and infinitesimal generator of a C0-semi-group of operators
A.3. Variations on the theme of injective cogenerators
A.3.1. Introduction
A.3.2. Review of injective cogenerators
A.3.3. Complements on coherent rings and modules
A.3.4. Injective cogenerators for finitely presented modules
A.3.5. Homo-, mono-, epi- and iso-morphisms of kernels
A.3.6. Quotient injective cogenerators
A.4. Complements of linear algebra
A.4.1. Presentations of a submodule and of a quotient module
A.4.2. Polynomial matrices and modules over K[s]T
A.4.3. Factorization of matrices over a Bézout domain
References
Index
EULA

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