Well-Posedness of Reset Control Systems as State-Dependent Impulsive Dynamical Systems

Abstract

Reset control systems are a special type of state-dependent impulsive dynamic systems, in which the time evolution depends both on continuous dynamics between resets and the discrete dynamics corresponding to the resetting times. This work is devoted to investigate well-posedness of reset control systems, taking as starting point the classical definition of Clegg and Horowitz. Well-posedness is related to the existence and uniqueness of solutions, and in particular to the resetting times to be well defined and distinct. A sufficient condition is developed for a reset system to have well-posed resetting times, which is also a sufficient condition for avoiding Zeno solutions and, thus, for a reset control system to be well-posed.