2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66937We investigate necessary and sufficient conditions under which a general nonlinear affine control system with outputs can be written as a gradient control system corresponding to some pseudo-Riemannian metric defined on the state space. The results rely on a suitable notion of compatibility of the system with respect to a given affine connection, and on the output behavior of the prolonged system and the gradient extension. The symmetric product associated with an affine connection plays a key role in the discussion.21 pages, no figuresOptimization and ControlDifferential Geometry93C10; 93B29; 53B05; 93B15text