Abstract
In this paper, we analyse the positive invariance of polyhedral sets with respect to the trajectories of linear dynamical systems represented in terms of delay-differential equations. An appropriate model transformation is employed, together with a matrix parametrization which allows exploiting system's structure by decoupling delay-dependent modes from delay-independent ones. Then, positive invariance conditions are obtained with explicit dependence on the delay, seen as a parameter. Connections and equivalence of positive invariance between the original and the transformed systems are established. The derived conditions are used to tackle the problem of computing a feedback control law which makes a given polyhedron positively invariant with respect to an input-delayed linear system. Illustrative examples complete the presentation.
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