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Stability Analysis of Nonlinear Systems

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  • © 2015

Overview

Authors:
  1. Vangipuram Lakshmikantham

    1. Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, USA

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  2. Srinivasa Leela

    1. State University of New York, Geneseo, Geneseo, USA

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  3. Anatoly A. Martynyuk

    1. National Academy of Sciences of Ukraine, Kiev, Ukraine

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  • 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

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

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xi
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  2. Inequalities

    • Vangipuram Lakshmikantham, Srinivasa Leela, Anatoly A. Martynyuk
    Pages 1-66

  3. Variation of Parameters and Monotone Technique

    • Vangipuram Lakshmikantham, Srinivasa Leela, Anatoly A. Martynyuk
    Pages 67-134

  4. Stability of Motion in Terms of Two Measures

    • Vangipuram Lakshmikantham, Srinivasa Leela, Anatoly A. Martynyuk
    Pages 135-200

  5. Stability of Perturbed Motion

    • Vangipuram Lakshmikantham, Srinivasa Leela, Anatoly A. Martynyuk
    Pages 201-252

  6. Stability In The Models of Real World Phenomena

    • Vangipuram Lakshmikantham, Srinivasa Leela, Anatoly A. Martynyuk
    Pages 253-309

  7. Back Matter

    Pages 311-329
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Keywords

About this book

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.





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)

Authors and Affiliations

  • Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, USA

    Vangipuram Lakshmikantham

  • State University of New York, Geneseo, Geneseo, USA

    Srinivasa Leela

  • National Academy of Sciences of Ukraine, Kiev, Ukraine

    Anatoly A. Martynyuk

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