Stability Conditions of Constrained Delay Systems via Positive Invariance

Abstract A delay system is represented by a linear difference equation. The system parameters and the delays are assumed to be unperfectly known. The output vector is perturbed by a bounded external disturbance vector. The addressed problem is to characterize conditions which guarantee that the output vector remains in a given domain defined by a set of symmetrical linear constraints. This problem is solved by imposing positive invariance conditions. These conditions also imply delay independent asymptotic stability of the associated deterministic system. The notion of distance to instability is then analyzed through the concept of stability radius. The possible use of these new robust stability conditions for controlling an input-output delay model is then presented. An application is finally proposed ; it concerns an inventory control problem for a simple production loop subject to constraints on inventory levels.