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© 2015

Stability Analysis of Nonlinear Systems

  • This references/text illuminates the most important results of the Lyapunov stability theory for several classes of equations of perturbed motion

  • It is first book that investigates stability theory in terms of two measures

  • It treats the theory of variety of inequalities, and demonstrates manifestations of the general Lyapunov method via scalar, vector and matrix-valued functions

Book

Part of the Systems & Control: Foundations & Applications book series (SCFA)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Vangipuram Lakshmikantham, Srinivasa Leela, Anatoly A. Martynyuk
    Pages 1-66
  3. Vangipuram Lakshmikantham, Srinivasa Leela, Anatoly A. Martynyuk
    Pages 67-134
  4. Vangipuram Lakshmikantham, Srinivasa Leela, Anatoly A. Martynyuk
    Pages 135-200
  5. Vangipuram Lakshmikantham, Srinivasa Leela, Anatoly A. Martynyuk
    Pages 201-252
  6. Vangipuram Lakshmikantham, Srinivasa Leela, Anatoly A. Martynyuk
    Pages 253-309
  7. Back Matter
    Pages 311-329

About this book

Introduction

The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clearly bringing out the underlying theme. It also demonstrates manifestations of the general Lyapunov method, showing how this technique can be adapted to various apparently diverse nonlinear problems. Furthermore it discusses the application of theoretical results to several different models chosen from real world phenomena, furnishing data that is particularly relevant for practitioners.

Stability Analysis of Nonlinear Systems is an invaluable single-sourse reference for industrial and applied mathematicians, statisticians, engineers, researchers in the applied sciences, and graduate students studying differential equations.

Keywords

inequalities variation of parameters stability of motion models of real world phenomena manifestations of the general Lyapunov method

Authors and affiliations

  1. 1.Department of Mathematical SciencesFlorida Institute of TechnologyMelbourneUSA
  2. 2.State University of New York, GeneseoGeneseoUSA
  3. 3.National Academy of Sciences of UkraineKievUkraine

Bibliographic information

  • Book Title Stability Analysis of Nonlinear Systems
  • Authors Vangipuram Lakshmikantham
    Srinivasa Leela
    Anatoly A. Martynyuk
  • Series Title Systems & Control: Foundations & Applications
  • Series Abbreviated Title Systems,Control:Foundat.,Applicat.(Birkhäuser)
  • DOI https://doi.org/10.1007/978-3-319-27200-9
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-27199-6
  • Softcover ISBN 978-3-319-80090-5
  • eBook ISBN 978-3-319-27200-9
  • Series ISSN 2324-9749
  • Series E-ISSN 2324-9757
  • Edition Number 2
  • Number of Pages XI, 329
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Dynamical Systems and Ergodic Theory
    Systems Theory, Control
  • Buy this book on publisher's site
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Reviews

“This text is published by Birkhäuser in the systems and control series. … The text is of most value to academics, researchers and students working in nonlinear systems.” (ACTC applied control technology consortium, actc-control.com, March, 2016)