Mathematical Problems in Engineering 
Volume 1 (1995), Issue 1, Pages 77-87
doi:10.1155/S1024123X95000081

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

Abstract

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.