An Introduction to InfiniteDimensional 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 frequencydomain methods, there is a need for an introductory text which treats both statespace and frequencydomain aspects in an integ...
Main Authors:  , 

Format:  eBook 
Language:  English 
Published: 
New York, NY
Springer New York
1995, 1995

Edition:  1st ed. 1995 
Series:  Texts in Applied Mathematics

Subjects:  
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 Frequencydomain spaces
 A.6.1 Laplace and Fourier transforms
 A.6.2 Frequencydomain 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 Rieszspectral 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 Inputoutput 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 finitetime interval
 6.2 The problem on the infinitetime interval
 6.3 Exercises
 6.4 Notes and references
 7 FrequencyDomain Descriptions
 7.1 The CallierDesoer class of scalar transfer functions
 7.2 The multivariable extension
 7.3 Statespace interpretations
 7.4 Exercises
 7.5 Notes and references
 8 Hankel Operators and the Nehari Problem
 8.1 Frequencydomain 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 FiniteDimensional Controller Synthesis
 9.1 Closedloop stability and coprime factorizations
 9.2 Robust stabilization of uncertain systems
 9.3 Robust stabilization under additive uncertainty
 9.4 Robust stabilization under normalized leftcoprimefactor uncertainty
 9.5 Robustness in the presence of small delays
 9.6 Exercises
 9.7 Notes and references
 A. Mathematical Background