Stability and stabilization of delay differential systems

The delay systems considered here are represented by linear delay differential equations. The system parameters and the delays are assumed to be imperfectly known. The instantaneous state vector is perturbed by a bounded external disturbance vector. The problem addressed is that of characterizing conditions that 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 the 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 the control of a multiple-delay MIMO differential model is then presented. Finally, an example is given.

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