Robust invariance for a class of time-delay systems with repeated eigenvalues

This paper focuses on the set invariance of linear systems characterized by transition matrices with repeated eigenvalues and geometric multiplicity inferior to the algebraic multiplicity. The goal is to model the variable delay affecting the input by polytopic type of uncertainty in order to preserve the linear convex description. It is shown that the embedding problem can be translated into a polytopic containment problem and a iterative approach to the construction of tight, low complexity embedding (simplex) is proposed. A design procedure for the construction of a robust positively invariant set for the system affected by time delay and subject to input and state constraints completes the paper.