We consider stability with respect to two measures of a difference inclusion, i.e., of a discrete-time dynamical system with the push-forward map being set-valued. We demonstrate that robust stability is equivalent to the existence of a smooth Lyapunov function and that, in fact, a continuous Lyapunov function implies robust stability. We also present a sufficient condition for robust stability...

Adaptive Horizon Model Predictive Control (AHMPC) is a scheme for varying as needed the horizon length of Model Predictive Control (MPC). Its goal is to achieve stabilization with horizons as small as possible so that MPC can be used on faster or more complicated dynamic processes. Beside the standard requirements of MPC including a terminal cost that is a control Lyapunov function, AHMPC requi...

This paper presents Lyapunov functions for proving stability of steady gliding motions for vehicles with hydrodynamic or aerodynamic forces and moments. Because of lifting forces and moments, system energy cannot be used as a Lyapunov function candidate. A Lyapunov function is constructed using a conservation law discovered by Lanchester in his classical work on phugoid-mode dynamics of an airp...