Prescribed-time control for impulsive systems with uncertainties via adaptive control

To present, there has been much research on prescribed-time stability (PTS) of uncertain systems, but the significant impulse factor has not been considered. Therefore, in this paper, the stability control problem of a class of impulsive systems with uncertainties within the prescribed time was studied by the Lyapunov functional approach. The comparison lemma was utilized and iteration was carried out for each impulsive interval to prove the PTS theorem for general impulsive systems with uncertainties. In addition, a time-varying adaptive controller in combination with the backstepping method was constructed for PTS of special impulsive strict-feedback systems with uncertainties, breaking through the dependence of traditional methods on uncertain parameters. Finally, a simulation example was used to verify the effectiveness and feasibility of the proposed method.