Abstract
A delay system is represented by a linear delay differential equation. The system parameters and the delays are assumed to be unperfectly known. The instantaneous state vector is perturbed by a bounded external disturbance vector. The addressed problem is to characterize conditions which guarantee that the trajectory of the instantaneous state vector remains in a domain defined by a set of symmetrical linear constraints. It is shown that positive invariance property can be used to solve this problem, and that positive invariance of a compact domain of the instantaneous state space implies delay independent asymptotic stability of the associated deterministic system. The possible use of these results for controlling a multiple delay MIMO differential model is then presented. An example is finally proposed.
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