Title: Co-design of aperiodic sampled-data min-jumping rules for linear impulsive, switched impulsive and sampled-data systems,
Abstract: Co-design conditions for the design of a jumping-rule and a sampled-data
control law for impulsive and impulsive switched systems subject to aperiodic
sampled-data measurements are provided. Semi-infinite discrete-time
Lyapunov-Metzler conditions are first obtained. As these conditions are
difficult to check and generalize to more complex systems, an equivalent
formulation is provided in terms of clock-dependent (infinite-dimensional)
matrix inequalities. These conditions are then, in turn, approximated by a
finite-dimensional optimization problem using a sum of squares based
relaxation. It is proven that the sum of squares relaxation is non conservative
provided that the degree of the polynomials is sufficiently large. It is
emphasized that acceptable results are obtained for low polynomial degrees in
the considered examples.