Abstract
The authors study the properties of some particular bounded sets with respect to trajectories of a linear continuous-time system with constrained input described by x(t)=Ax(t)+c(t), where c(t) epsilon Omega , a compact set, and matrix e/sup tA/ has the property of leaving a proper cone K positively invariant, that is, e/sup tA/ K contained in/implied by K. Necessary and sufficient conditions guaranteeing that some bounded sets D(K; a,b) obtained from the intersection of shifted cones are positively invariant with respect to the considered system are given. The external behavior of motions is studied in terms of attractivity and contractivity of the set D(K; a,b). The proposed results are applied to the study of the saturated state feedback regulator problem.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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