About Lyapunov functionals construction for difference equations with continuous time.
The author considers difference equations (in continuous time) of the form \[ x(t+h_0)=F(t,x(t),x(t-h_1),x(t-h_2),\ldots) \] with the initial condition \(x(\theta)=\phi(\theta)\) for \(\theta\in [t_0-h_0-\max_{j\geq 1}h_j,t_0]\). Under some condition on \(F\) he proves a stability criterion in terms of the existence of a Lyapunov functional. The second part of the paper is devoted to two ways to construct such a Lyapunov functional.
difference equations with continuous time
scientific article; zbMATH DE number 2140773