Fourier Series in Control Theory

  • Vilmos Komornik
  • Paloa Loreti

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

About this book

Introduction

Advance Praise for Fourier Series in Control Theory:

It has been known since 1967 that a wide variety of sets of complex exponential functions play an important role in the control theory of systems governed by partial differential equations. Up until now, the relevant literature has been scattered among various journal articles, a survey paper by myself in SIAM Review in 1978, and the book, Families of Exponentials, by S. Avdonin and S. Ivanov (1995). Fourier Series in Control Theory successfully gathers all of the available theory of these "nonharmonic Fourier series" in one place, combining published results with new results, to create a unique source of such material for practicing applied mathematicians, engineers, and other scientific professionals.

- David Russell, Virginia Polytechnic Institute and State University

This monograph will be of interest to experts and researchers, as well as graduate students in such courses as control series and harmonic analysis. Starting with an overview of the problems of observability, controllability, and stabilization of linear systems and their interconnections, the text contains complete proofs along with a short, simplified, presentation of some properties of Bessel functions for the convenience of the reader. Only basic knowledge of functional analysis is required.

Keywords

control control theory functional analysis partial differential equation stabilization

Authors and affiliations

  • Vilmos Komornik
    • 1
  • Paloa Loreti
    • 2
  1. 1.Institut de Recherche Mathématique AvancéeUniversité Louis Pasteur et CNRSStrasbourg CedexFrance
  2. 2.Dipartimento di Metodi e Modelli Matematici per le Scienze ApplicateUniversitá degli Studi di Roma “La Sapienza”RomaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/b139040
  • Copyright Information Springer Science+Business Media, Inc. 2005
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-22383-4
  • Online ISBN 978-0-387-27408-9
  • Series Print ISSN 1439-7382
  • About this book