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An Introduction to Infinite-Dimensional Linear Systems Theory

Infinite dimensional systems is now an established area of research. Given the recent trend in systems theory and in applications towards a synthesis of time- and frequency-domain methods, there is a need for an introductory text which treats both state-space and frequency-domain aspects in an integ...

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Bibliographic Details
Main Authors: Curtain, Ruth F., Zwart, Hans (Author)
Format: eBook
Language:English
Published: New York, NY Springer New York 1995, 1995
Edition:1st ed. 1995
Series:Texts in Applied Mathematics
Subjects:
Mathematical Analysis
Analysis
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • A.1 Complex analysis
  • A.2 Normed linear spaces
  • A.2.1 General theory
  • A.2.2 Hilbert spaces
  • A.3 Operators on normed linear spaces
  • A.3.1 General theory
  • A.3.2 Operators on Hilbert spaces
  • A.4 Spectral theory
  • A.4.1 General spectral theory
  • A.4.2 Spectral theory for compact normal operators
  • A.5 Integration and differentiation theory
  • A.5.1 Integration theory
  • A.5.2 Differentiation theory
  • A.6 Frequency-domain spaces
  • A.6.1 Laplace and Fourier transforms
  • A.6.2 Frequency-domain spaces
  • A.6.3 The Hardy spaces
  • A.7 Algebraic concepts
  • A.7.1 General definitions
  • A.7.2 Coprime factorizations over principal ideal domains
  • A.7.3 Coprime factorizations over commutative integral domains
  • References
  • Notation
  • 1 Introduction
  • 1.1 Motivation
  • 1.2 Systems theory concepts in finite dimensions
  • 1.3 Aims of this book
  • 2 Semigroup Theory
  • 2.1 Strongly continuous semigroups
  • 2.2 Contraction and dual semigroups
  • 2.3 Riesz-spectral operators
  • 2.4 Delay equations
  • 2.5 Invariant subspaces
  • 2.6 Exercises
  • 2.7 Notes and references
  • 3 The Cauchy Problem
  • 3.1 The abstract Cauchy problem
  • 3.2 Perturbations and composite systems
  • 3.3 Boundary control systems
  • 3.4 Exercises
  • 3.5 Notes and references
  • 4 Inputs and Outputs
  • 4.1 Controllability and observability
  • 4.2 Tests for approximate controllability and observability
  • 4.3 Input-output maps
  • 4.4 Exercises
  • 4.5 Notes and references
  • 5 Stability, Stabilizability, and Detectability
  • 5.1 Exponential stability
  • 5.2 Exponential stabilizability and detectability
  • 5.3 Compensator design
  • 5.4 Exercises
  • 5.5 Notes and references
  • 6 Linear Quadratic Optimal Control
  • 6.1 The problem on a finite-time interval
  • 6.2 The problem on the infinite-time interval
  • 6.3 Exercises
  • 6.4 Notes and references
  • 7 Frequency-Domain Descriptions
  • 7.1 The Callier-Desoer class of scalar transfer functions
  • 7.2 The multivariable extension
  • 7.3 State-space interpretations
  • 7.4 Exercises
  • 7.5 Notes and references
  • 8 Hankel Operators and the Nehari Problem
  • 8.1 Frequency-domain formulation
  • 8.2 Hankel operators in the time domain
  • 8.3The Nehari extension problem for state linear systems
  • 8.4 Exercises
  • 8.5 Notes and references
  • 9 Robust Finite-Dimensional Controller Synthesis
  • 9.1 Closed-loop stability and coprime factorizations
  • 9.2 Robust stabilization of uncertain systems
  • 9.3 Robust stabilization under additive uncertainty
  • 9.4 Robust stabilization under normalized left-coprime-factor uncertainty
  • 9.5 Robustness in the presence of small delays
  • 9.6 Exercises
  • 9.7 Notes and references
  • A. Mathematical Background

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