A sampled-data system with sampling interval lengths selected from a finite set is considered. Stabilizability of the system via feedbacks associated with sampling interval lengths is studied, and conditions for stabilizability involving "pre-contractiveness", "contractiveness", and "positive definiteness" of a finite set of matrices are given. Included in these results is a generalization of a theorem by P. Stein stating that for a real square matrix H, lim,_. H" 0 if and only if there is a symmetric matrix Q such that Q-HrQH is positive definite. Finally, some results concerning a choice of feedbacks which will produce stability are presented.
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