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  • © 2019

Qualitative Analysis of Set-Valued Differential Equations

Birkhäuser

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  • First book on the theoretical foundations of modeling real-world phenomena by a set of differential equations

  • Focusses on differential equations with uncertainty

  • Written for the experts working in the ?eld of qualitative analysis of di?erential and other types of equations

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USD 89.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-07644-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
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USD 119.99
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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xiii
  2. General Properties of Set-Valued Equations

    • Anatoly A. Martynyuk
    Pages 1-45
  3. Analysis of Continuous Equations

    • Anatoly A. Martynyuk
    Pages 47-84
  4. Discrete-Time Systems with Switching

    • Anatoly A. Martynyuk
    Pages 85-101
  5. Qualitative Analysis of Impulsive Equations

    • Anatoly A. Martynyuk
    Pages 103-122
  6. Stability of Systems with Aftereffect

    • Anatoly A. Martynyuk
    Pages 123-134
  7. Impulsive Systems with Aftereffect

    • Anatoly A. Martynyuk
    Pages 135-149
  8. Dynamics of Systems with Causal Operator

    • Anatoly A. Martynyuk
    Pages 151-171
  9. Finite-Time Stability of Standard Systems Sets

    • Anatoly A. Martynyuk
    Pages 173-187
  10. Back Matter

    Pages 189-198

About this book

The book discusses set-valued differential equations defined in terms of the Hukuhara derivative. Focusing on equations with uncertainty, i.e., including an unknown parameter, it introduces a regularlization method to handle them.  The main tools for qualitative analysis are the principle of comparison of Chaplygin – Wazhewsky, developed for the scalar, vector and matrix-valued Lyapunov functions and the method of nonlinear integral inequalities, which are used to establish existence, stability or boundedness.

Driven by the question of how to model real processes using a set-valued of differential equations, the book lays the theoretical foundations for further study in this area. It is intended for experts working in the field of qualitative analysis of differential and other types of equations.

Keywords

  • set equations
  • regularization of uncertain set equations
  • stability
  • asymptotic stability
  • boundedness
  • mixed minkowski volumes
  • ordinary differential equations

Authors and Affiliations

  • Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine

    Anatoly A. Martynyuk

Bibliographic Information

  • Book Title: Qualitative Analysis of Set-Valued Differential Equations

  • Authors: Anatoly A. Martynyuk

  • DOI: https://doi.org/10.1007/978-3-030-07644-3

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2019

  • Hardcover ISBN: 978-3-030-07643-6

  • eBook ISBN: 978-3-030-07644-3

  • Edition Number: 1

  • Number of Pages: XIII, 198

  • Number of Illustrations: 1 illustrations in colour

  • Topics: Differential Equations, Systems Theory, Control

Buying options

eBook
USD 89.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-07644-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Hardcover Book
USD 119.99
Price excludes VAT (USA)