Impulsive Input-to-State Stabilization of an Ensemble

Abstract

We consider an ensemble of trajectories generated by a linear differential equation subjected to disturbance and parameterized by the initial state. The scalar output of the system is the volume comprised by the states of the whole ensemble. Already the unperturbed dynamics is assumed to be unstable. In order to stabilize the system with unknown inputs in the ISS sense we design impulsive control actions based in the output signal and establish conditions under which the system possesses the ISS property under these impulsive actions.