Integral Equations and Stability of Feedback Systems

Name: Integral Equations and Stability of Feedback Systems
Brand: Academic Press
Price: 62.95 EUR
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Corduneanu(Herausgeber*in)

Academic Press

Erschienen am 14. Mai 2014

249 Seiten

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978-0-08-095613-8 (ISBN)

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Front Cover
Integral Equations and Stability of Feedback Systems
Copyright Page
Contents
Preface
Chapter 1. Preliminaries
1.1 Some Function Spaces
1.2 A Fixed-Point Theorem
1.3 Fourier and Laplace Transforms
1.4 A Factorization Problem
Exercises
Chapter 2. Admissibility and Hammerstein Equations
2.1 Admissibility and Continuity
2.2 Admissibility of the Pair (Cg, CG) with Respect to the Volterra Operator
2.3 Admissibility of the Pair (Cg, Cl)
2.4 Admissibility of the Pair (Lg8, CG)
2.5 Admissibility of the Pair (LP, CG), 1 & p & 8
2.6 Admissibility of the Pair (Lg8, LG8)
2.7 Admissibility with Respect to the Convolution Operator
2.8 Review of Other Admissibility Results
2.9 Admissibility for Differential Systems
2.10 Integral Equations in CG
2.11 Perturbed Integral Equations in CG
2.12 Existence of Convergent Solutions
2.13 Further Existence Results in CG
2.14 Convolution Equations
2.15 Existence of Measurable Solutions
Exercises
Bibliographical Notes
Chapter 3. Frequency Techniques and Stability
3.1 General Remarks and Statement of Some Problems
3.2 Equation (1.1) with an Integrable Kernel
3.3 Equation (1.1) with k(t) + ? Integrable, ? & 0
3.4 Further Investigation of the Preceding Case
3.5 Another Case of a Nonintegrable Kernel
3.6 A Stability Result in the Vector Case
3.7 An Integro-Differential Equation
3.8 Existence of L2 Solutions
3.9 Control Systems with Time Lag
3.10 A Result of Yakubovitch
3.11 Energetic Stability
3.12 A Criterion for LP Stability
Exercises
Bibliographical Notes
Chapter 4. Wiener-Hopf Equations
4.1 A Special Class of Kernels
4.2 Equation (WH) with Index Zero
4.3 Equation (WH) with Positive Index
4.4 Equation (WH) with Negative Index
4.5 Some Examples
4.6 Perturbed Equations
Exercises
Bibliographical Notes
Chapter 5. Further Methods and Topics
5.1 Some Results of Levin
5.2 A System Occurring in the Dynamics of Nuclear Reactors
5.3 A Positivity Condition for the Kernel
5.4 Linearization of Volterra Integral Equations
5.5 Volterra-Stieltjes Integral Equations
5.6 Tauberian Results
Exercises
Bibliographical Notes
References
Author Index
Subject Index

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