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Co-design conditions for the design of a jumping-rule and a sampled-datacontrol law for impulsive and impulsive switched systems subject to aperiodicsampled-data measurements are provided. Semi-infinite discrete-timeLyapunov-Metzler conditions are first obtained. As these conditions aredifficult to check and generalize to more complex systems, an equivalentformulation is provided in terms of clock-dependent (infinite-dimensional)matrix inequalities. These conditions are then, in turn, approximated by afinite-dimensional optimization problem using a sum of squares basedrelaxation. It is proven that the sum of squares relaxation is non conservativeprovided that the degree of the polynomials is sufficiently large. It isemphasized that acceptable results are obtained for low polynomial degrees inthe considered examples.

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