Impulsive Discontinuous Stabilization of the Brockett Integrator

摘要

Recently, many researchers have undertaken to obtain classes of admissible controls that stabilize nonlinear controllable dynamic systems. Sampling control was shown to be one of those classes. In this work, impulsive control is proposed to be applied. This control is interesting in theoretical investigations and important in applications. The problem is stated on the basis of generalized functions that are later reduced to the form used in modern impulsive system theory. Various types of impulse, impulse discontinuous, and discontinuous stabilizing controls are constructed using the Brockett integrator as an example. The obtained results are illustrated by numerical simulations.