Mathematical Problems in Engineering
Volume 1 (1995), Issue 1, Pages 77-87

Feedback control of time-delay systems with bounded control and state

M. Dambrine, J. P. Richard, and P. Borne

Ecole Centrale de Lille, LAIL-URA CNRS D 1440, BP 48, 59651 Villeneuve d'Ascq, Cedex, France

Received 14 October 1994

Copyright © 1995 M. Dambrine et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper is concerned with the problem of stabilizing linear time-delay systems under state and control linear constraints. For this, necessary and sufficient conditions for a given non-symmetrical polyhedral set to be positively invariant are obtained. Then existence conditions of linear state feedback control law respecting the constraints are established, and a procedure is given in order to calculate such a controller. The paper concerns memoryless controlled systems but the results can be applied to cases of delayed controlled systems. An example is given.