1 Positive Constrained Control for Continuous-time Fractional Positive Systems F. Mesquine, A. Benzaouia, A. Hmamed, M. Benhayoun and F. Tadeo Abstract The stabilization problem for fractional linear continuous-time systems having bounded positive control is solved, with the additional condition of non negativity of the states. Thus, a methodology to develop state-feedback controllers is proposed, based on Linear Programming conditions. An illustrative example is provided to show the usefulness of the results. Keywords: Fractional systems, positive systems, stabilization, bounded controls, linear program- ming. I. INTRODUCTION The first introduction of fractional derivative was proposed by Liouville and Riemann at the XIX century as pointed out in [20]. Background works on mathematical fractional calculus can be found in [24], [20], [22]. The first work on control of fractional systems was given in [22]. Recent works on stability and robust stability were studied extensively in [23], [15], [16], [21]. Most of these papers use algebraic stability conditions. A few papers use the Lyapunov concept to deal with the problem of analysis stability of fractional systems, for example [17]. We can emphasize [25], that presents an interesting discussion about the meaning of Lyapunov function concept for fractional systems. Besides, a condition of stability similar to ordinary systems is obtained for a quadratic Lyapunov function candidate. New developments based on Lyapunov equations can be found in [8]. This paper concentrates on a specific class of fractional systems: those with nonnegative states. In the literature, systems with non negative states are referred as positive systems (see [14] for general references). Nonnegative states appear in many practical problems, when the states represent Mesquine, Benzaouia and Benhayoun are with EACPI, URAC 28, University Cadi Ayyad, Faculty of Science Semlalia, BP 2390, Marrakech, Morocco (e-mail:mesquine, benzaouia, benhayoun@uca.ma). Hmamed is with LESSI, University Mohamed Ben Abdellah, Faculty of Sciences Dhar El Mhraz, BP 1796, Fes, Morocco (e-mail:hmamed abdelaziz@yahoo.fr). Tadeo is with Dpto. Ingenieria de Sistemas y Automatica, Universidad de Valladolid, 47005 Valladolid, Spain (e- mail:fernando@autom.uva.es). September 14, 2012 DRAFT 13 th International conference on Sciences and Techniques of Automatic control & computer engineering December 17-19, 2012, Monastir, Tunisia STA'2012- -2 , pages - Academic Publication Center of Tunis, Tunisia