Logo - springer
Slogan - springer

Engineering - Control Engineering | Lyapunov Functionals and Stability of Stochastic Difference Equations

Lyapunov Functionals and Stability of Stochastic Difference Equations

Shaikhet, Leonid

2011, VI, 284p. 119 illus., 117 illus. in color.

Available Formats:

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.


(net) price for USA

ISBN 978-0-85729-685-6

digitally watermarked, no DRM

Included Format: PDF and EPUB

download immediately after purchase

learn more about Springer eBooks

add to marked items


Hardcover version

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.


(net) price for USA

ISBN 978-0-85729-684-9

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days

add to marked items

  • Detailed description of Lyapunov functional construction will allow researchers to analyse stability results for hereditary systems more easily
  • Profuse analytical and numerical examples help to explain the methods used
  • Demonstrates a method that can be usefully applied in economic, mechanical, biological and ecological systems


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.


Content Level » Research

Keywords » Control Theory - Lyapunov Functionals Construction - Numerical Analysis - Stability Theory - Stochastic Difference Equations

Related subjects » Control Engineering - Dynamical Systems & Differential Equations - Mathematics - Mechanics - Probability Theory and Stochastic Processes

Table of contents / Preface / Sample pages 

Popular Content within this publication 



Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Control.