On the Polyhedral Set-Invariance Conditions for Time-Delay Systems

In this paper the concept of set invariance for time-delay systems is introduced with a specific attention to the linear discrete-time case. We are interested in the definition of a D(elay)-invariant set with respect to a bounded polyhedral subset of the state-space. D-invariance conditions are derived based on the Minkowski addition in a first stage, and subsequently translated in feasibility-based tests in order to obtain an efficient computation time