2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123159We provide general methods for explicitly constructing strict Lyapunov functions for fully nonlinear slowly time-varying systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily exponentially stable. This complements our previous Lyapunov function constructions for rapidly time-varying dynamics. We also explicitly construct input-to-state stable Lyapunov functions for slowly time-varying control systems. We illustrate our findings by constructing explicit Lyapunov functions for a pendulum model, an example from identification theory, and a perturbed friction model.Accepted for publication in Mathematics of Control, Signals, and Systems (MCSS) on November 20, 2006Optimization and Control93D30text