Co-design of aperiodic sampled-data min-jumping rules for linear impulsive, switched impulsive and sampled-data systems

An aperiodic sampled-data min-jumping rule is proposed for linear impulsive systems, a class of systems encompassing switched and sampled-data systems as particular cases. Several sufficient co-design conditions characterizing the stabilization of a given linear impulsive system subject to the considered min-jumping rule and a sampled-data state-feedback controller are formulated in terms of discretetime Lyapunov-Metzler conditions. These conditions are then exactly reformulated as clock-dependent conditions known to be more convenient to verify and that allow for an immediate extension of the results to uncertain systems and to performance analysis. Several examples pertaining on sampled-data control of switched and impulsive systems are given for illustration.