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

Michel Dambrine (1) , Jean-Pierre Richard (2, 3) , Pierre Borne (3, 2)

1 LAMIH - Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201
2 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
3 Centrale Lille

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

Domaines: Informatique [cs]; Automatique; Mathématiques [math]; Systèmes dynamiques [math.DS]; Sciences de l'ingénieur [physics]; Automatique / Robotique

Michel Dambrine, Jean-Pierre Richard, Pierre Borne. Feedback control of time-delay systems with bounded control and state. Mathematical Problems in Engineering, 1995, 1 (1), pp.77-87. ⟨10.1155/S1024123X95000081⟩. ⟨hal-02560687⟩