2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128607The paper presents the generalized persistency of excitation conditions. They are not only valid for much broader range of applications than their classical counterparts but also elegantly prove the validity of the latter. The novelty and the significance of the approach presented in this publication is due to employing the time averaging technique.General Mathematics93D15; 93D20; 93B35text