Variational lyapunov method for discrete hybrid systems

In this paper, we consider the difference equation Δy(n) = f(n,y), y(n0) = x0. We relax the smoothness condition on f with respect to y that was imposed in [1] and obtain an improved version of the nonlinear variation of parameter (NVP) formula. We then develop a variational Lyapunov method (VLM) for difference equations and apply it to discrete hybrid systems.