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Frequency Domain Criteria for Absolute Stability

A Delay-integral-quadratic Constraints Approach

  • Dmitry Altshuller

Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 432)

Table of contents

  1. Front Matter
    Pages 1-8
  2. Dmitry Altshuller
    Pages 1-24
  3. Dmitry Altshuller
    Pages 25-41
  4. Dmitry Altshuller
    Pages 43-80
  5. Dmitry Altshuller
    Pages 81-115
  6. Back Matter
    Pages 0--1

About this book

Introduction

Frequency Domain Criteria for Absolute Stability focuses on recently-developed methods of delay-integral-quadratic constraints to provide criteria for absolute stability of nonlinear control systems. The known or assumed properties of the system are the basis from which stability criteria are developed. Through these methods, many classical results are naturally extended, particularly to time-periodic but also to nonstationary systems. Mathematical prerequisites including Lebesgue-Stieltjes measures and integration are first explained in an informal style with technically more difficult proofs presented in separate sections that can be omitted without loss of continuity.
The results are presented in the frequency domain – the form in which they naturally tend to arise. In some cases, the frequency-domain criteria can be converted into computationally tractable linear matrix inequalities but in others, especially those with a certain geometric interpretation, inferences concerning stability can be made directly from the frequency-domain inequalities.
The book is intended for applied mathematicians and control systems theorists. It can also be of considerable use to mathematically-minded engineers working with nonlinear systems.

Keywords

Automatic Control Control Theory Frequency-domain Methods Gradient Nonlinearities Monotone Nonlinearities Quasimonotone Nonlinearities System Stability

Authors and affiliations

  • Dmitry Altshuller
    • 1
  1. 1.RiversideUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-4234-8
  • Copyright Information Springer-Verlag London 2013
  • Publisher Name Springer, London
  • eBook Packages Engineering
  • Print ISBN 978-1-4471-4233-1
  • Online ISBN 978-1-4471-4234-8
  • Series Print ISSN 0170-8643
  • Series Online ISSN 1610-7411
  • Buy this book on publisher's site
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