Construction of Lyapunov functionals for coupled differential and continuous time difference equations

2013 ◽  
Author(s):  
Frederic Mazenc ◽  
Hiroshi Ito ◽  
Pierdomenico Pepe
Keyword(s):  
Difference Equations ◽  
Continuous Time ◽  
Time Difference ◽  
Lyapunov Functionals

Exponential L2-stability for a class of linear systems governed by continuous-time difference equations

Automatica ◽  
2014 ◽  
Vol 50 (12) ◽  
pp. 3299-3303 ◽  
Author(s):  
Sérine Damak ◽  
Michael Di Loreto ◽  
Warody Lombardi ◽  
Vincent Andrieu
Keyword(s):  
Linear Systems ◽  
Difference Equations ◽  
Continuous Time ◽  
Time Difference

GENERAL METHOD OF LYAPUNOV FUNCTIONALS CONSTRUCTION IN STABILITY INVESTIGATIONS OF NONLINEAR STOCHASTIC DIFFERENCE EQUATIONS WITH CONTINUOUS TIME

2005 ◽  
Vol 05 (02) ◽  
pp. 175-188 ◽  
Author(s):  
LEONID SHAIKHET
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Continuous Time ◽  
Type Theorem ◽  
Volterra Equations ◽  
Lyapunov Functionals ◽  
Stochastic Difference Equation ◽  
Stochastic Difference Equations ◽  
After Effect ◽  
General Method

The general method of Lyapunov functionals construction has been developed during the last decade for stability investigations of stochastic differential equations with after-effect and stochastic difference equations. After some modification of the basic Lyapunov type theorem this method was successfully used also for difference Volterra equations with continuous time. The latter often appear as useful mathematical models. Here this method is used for a stability investigation of some nonlinear stochastic difference equation with continuous time.

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