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Systems & Control: Foundations & Applications

Stability Theory for Dynamic Equations on Time Scales

Authors: Martynyuk, Anatoly A.

  • This book presents a systematic study of stability theory of dynamic equations on time scales and exhibits the advantage of matrix-valued of Lyapunov functions
  • It treats the theory of dynamic integral inequalities in the underlying theme
  • This volume demonstrates the manifestations of general comparison principle by showing how this effective technique can be adapted to study various apparently diverse nonlinear  dynamics problems. 
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eBook 79,72 €
price for Spain (gross)
  • ISBN 978-3-319-42213-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
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  • Immediate eBook download after purchase
Hardcover 98,79 €
price for Spain (gross)
  • ISBN 978-3-319-42212-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems.In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. In the book “Men of Mathematics,” 1937, E.T.Bell wrote: “A major task of mathematics today is to harmonize the continuous and the discrete, to include them in one comprehensive mathematics, and to eliminate obscurity from both.”Mathematical analysis on time scales accomplishes exactly this. 
This research has potential applications in such areas as theoretical and applied mechanics, neurodynamics, mathematical biology and finance among others.

Table of contents (5 chapters)

  • Elements of Time Scales Analysis

    Martynyuk, Anatoly A.

    Pages 1-23

    Preview Buy Chapter 30,19 €
  • Method of Dynamic Integral Inequalities

    Martynyuk, Anatoly A.

    Pages 25-84

    Preview Buy Chapter 30,19 €
  • Lyapunov Theory for Dynamic Equations

    Martynyuk, Anatoly A.

    Pages 85-144

    Preview Buy Chapter 30,19 €
  • Comparison Method

    Martynyuk, Anatoly A.

    Pages 145-183

    Preview Buy Chapter 30,19 €
  • Applications

    Martynyuk, Anatoly A.

    Pages 185-214

    Preview Buy Chapter 30,19 €

Buy this book

eBook 79,72 €
price for Spain (gross)
  • ISBN 978-3-319-42213-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 98,79 €
price for Spain (gross)
  • ISBN 978-3-319-42212-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Stability Theory for Dynamic Equations on Time Scales
Authors
Series Title
Systems & Control: Foundations & Applications
Copyright
2016
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-42213-8
DOI
10.1007/978-3-319-42213-8
Hardcover ISBN
978-3-319-42212-1
Series ISSN
2324-9749
Edition Number
1
Number of Pages
XI, 223
Topics