Lyapunov Functionals and Stability of Stochastic Difference Equations

• Main Author: Shaikhet, Leonid (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London, 2011.
• Subjects: Engineering.; Difference equations.; Functional equations.; Calculus of variations.; Probabilities.; Biomathematics.; Vibration.; Dynamical systems.; Dynamics.; Control engineering.; Control.; Difference and Functional Equations.; Calculus of Variations and Optimal Control; Optimization.; Mathematical and Computational Biology.; Probability Theory and Stochastic Processes.; Vibration, Dynamical Systems, Control.

  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 Lyapun...

Table of Contents:

• Lyapunov-type Theorems and Procedure for Lyapunov Functional Construction
• Illustrative Example
• Linear Equations with Stationary Coefficients
• Linear Equations with Nonstationary Coefficients
• Some Peculiarities of the Method
• Systems of Linear Equations with Varying Delays
• Nonlinear Systems
• Volterra Equations of the Second Type
• Difference Equations with Continuous Time
• Difference Equations as Difference Analogues of Differential Equations.