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Resolution Space, Operators and Systems

  • R.¬†Saeks

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 82)

Table of contents

  1. Front Matter
    Pages I-X
  2. R. Saeks
    Pages 1-60
  3. R. Saeks
    Pages 61-113
  4. R. Saeks
    Pages 114-154
  5. R. Saeks
    Pages 155-203
  6. Back Matter
    Pages 204-270

About this book

Introduction

If one takes the intuitive point of view that a system is a black box whose inputs and outputs are time functions or time series it is natural to adopt an operator theoretic approach to the stUdy of such systems. Here the black box is modeled by an operator which maps an input time function into an output time function. Such an approach yields a unification of the continuous (time function) and discrete (time series) theories and simultaneously allows one to formulate a single theory which is valid for time-variable distributed and nonlinear systems. Surprisingly, however, the great potential for such an approach has only recently been realized. Early attempts to apply classical operator theory typically having failed when optimal controllers proved to be non-causal, feedback systems unstable or coupling networks non-lossless. Moreover, attempts to circumvent these difficulties by adding causality or stability constraints to the problems failed when it was realized that these time based concepts were undefined and; in fact, undefinable; in the Hilbert and Banach spaces of classical operator theory.

Keywords

Operators control dynamische Systeme networks time

Authors and affiliations

  • R.¬†Saeks
    • 1
  1. 1.Dept. of Electrical EngineeringUniversity of Notre DameNotre DameUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-80735-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 1973
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-06155-7
  • Online ISBN 978-3-642-80735-0
  • Series Print ISSN 0075-8442
  • Buy this book on publisher's site