Stabilisation of controlled positive delayed continuous-time systems

Abstract

This article solves the stabilisation problem by output feedback control for linear continuous-time systems with delay. This technique can be applied for both positive systems and controlled positive systems (systems becoming positive in closed-loop). The synthesis of feedback controllers is solved in terms of linear programs, extending the solution also to stabilisation with bounded control and stabilisation by controllers with the memory of the delayed state. The proposed conditions do not involve the value of the delay. Some examples illustrate the proposed approach.

Keywords:

• positive systems
• delay systems
• stabilisation
• output feedback control
• bounded controls
• linear programming

Acknowledgements

This work was funded by the ‘Convocatoria de Ayudas para la Estancia de Investigadores’ of the University of Valladolid, AECID project A/7882/07 and MiCInn project DPI2007-66718-C04-02.