Non-conservative ultimate bound estimation in LTI perturbed systems

A closed formula for ultimate bound estimation in LTI systems with non-vanishing perturbations is presented. The formula, based on geometrical properties of the system, provides an alternative to Lyapunov's second method based study. Although it is not proven that the bound obtained is always less conservative than the Lyapunov's bound, some examples are introduced where the estimations are significantly improved. An extension of the idea for nonlinear systems is also sketched.