Robust stability of impulsive systems: A functional-based approach

An improved functional-based approach for the stability analysis of linear uncertain impulsive systems relying on Lyapunov looped-functionals is provided. Looped functionals are peculiar functionals that allow to encode discrete-time stability criteria into continuous-time conditions and to consider non-monotonic Lyapunov functions along the trajectories of the impulsive system. Unlike usual discrete-time stability conditions, the obtained ones are convex in the system matrices, an important feature for extending the results to uncertain systems. It is emphasized in the examples that the proposed approach can be applied to a class of systems for which existing approaches are inconclusive, notably systems having unstable continuous and discrete dynamics.