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 n → ∞ Hⁿ = 0 if and only if there is a symmetric matrix Q such that Q - HT QH is positive definite. Finally, some results concerning a choice of feedbacks which will produce stability are presented.
No takes yet. Share an insight, caveat, or question.
David P. Stanford (1979) studied this question.
Synapse has enriched one closely related paper. Consider it for comparative context: