Elsevier

Automatica

Volume 33, Issue 3, March 1997, Pages 347-354
Automatica

Paper
Stability and stabilization of delay differential systems☆

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Abstract

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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☆

A preliminary version of this paper was presented at the 13th IFAC World Congress, which was held in San Francisco, U.S.A. during 30 June–5 July 1996. The Published Proceedings of this IFAC meeting may be ordered from the Customer Support Departments of the Elsevier Science Regional Sales Offices (see p. ii of Automatica) or from Elsevier Science Ltd, The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, U.K. This paper was recommended for publication in revised form by Associate Editor O. Staffans under the direction of Editor Ruth F. Curtain.

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