The classical Lyapunov analysis of stable fixed points is extended to perturbed dynamical systems that may not have any fixed point due to perturbations. Practical stability is meant here to assess the convergence of such systems. This is achieved by investigating a parametric optimization problem encoding some worst-case Lie derivative. Key properties of this parametric optimization problem are formulated. The proposed framework is finally applied to a class of perturbed linear systems tracking a highly nonlinear reference.