Lyapunov Functionals and Stability of Stochastic Difference Equations

  • Leonid Shaikhet

Table of contents

  1. Front Matter
    Pages I-XII
  2. Leonid Shaikhet
    Pages 11-21
  3. Leonid Shaikhet
    Pages 23-59
  4. Leonid Shaikhet
    Pages 79-108
  5. Leonid Shaikhet
    Pages 109-125
  6. Leonid Shaikhet
    Pages 127-190
  7. Leonid Shaikhet
    Pages 191-225
  8. Leonid Shaikhet
    Pages 227-281
  9. Back Matter
    Pages 355-370

About this book

Introduction

 

Hereditary systems (or systems with either delay or after-effects) are widely used to model processes in physics, mechanics, control, economics and biology. An important element in their study is their stability.

Stability conditions for difference equations with delay can be obtained using Lyapunov functionals.

Lyapunov Functionals and Stability of Stochastic Difference Equations describes the general method of Lyapunov functionals construction to investigate the stability of discrete- and continuous-time stochastic Volterra difference equations. The method allows the investigation of the degree to which the stability properties of differential equations are preserved in their difference analogues.

The text is self-contained, beginning with basic definitions and the mathematical fundamentals of Lyapunov functionals construction and moving on from particular to general stability results for stochastic difference equations with constant coefficients. Results are then discussed for stochastic difference equations of linear, nonlinear, delayed, discrete and continuous types. Examples are drawn from a variety of physical and biological systems including inverted pendulum control, Nicholson's blowflies equation and predator-prey relationships.

Lyapunov Functionals and Stability of Stochastic Difference Equations is primarily addressed to experts in stability theory but will also be of use in the work of pure and computational mathematicians and researchers using the ideas of optimal control to study economic, mechanical and biological systems.

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Keywords

Control Theory Lyapunov Functionals Construction Numerical Analysis Stability Theory Stochastic Difference Equations

Authors and affiliations

  • Leonid Shaikhet
    • 1
  1. 1.Department of Higher MathematicsDonetsk State University of ManagementDonetskUkraine

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-85729-685-6
  • Copyright Information Springer-Verlag London Limited 2011
  • Publisher Name Springer, London
  • eBook Packages Engineering
  • Print ISBN 978-0-85729-684-9
  • Online ISBN 978-0-85729-685-6
  • About this book