Global Mittag-Leffler output feedback stabilization for nonlinear fractional-order system with known growth rate Nadhem ECHI Gafsa University, Faculty of Sciences of Gafsa Department of Mathematics, Zarroug Gafsa 2112 Tunisia e-mail: nadhemechi fsg@yahoo.fr Abstract Stabilization of fractional-order nonlinear systems is studied. This paper investigates the problem of global Mittag Leffler stabilization by state and output-feedback for a family of nonlinear Caputo fractional-order systems written in triangular form satisfying linear growth conditions. By using a Lyapunov function, global Mittag-Leffler stability of the closed-loop systems is achieved. Finally, simulation results dealing with typical bioreactor example, are given to illustrate that the proposed design procedures are very efficient and simple. Mathematics Subject Classification. 93C10, 93D15, 93D20. Keywords. Caputo derivative, observer design, Mittag-Leffler stability, Lyapunov func- tion. 1 Introduction Fractional calculus is a concept of integrals and derivatives of arbitrary non-integer order. It is one of the more powerful tools to deal with complex phenomena. Moreover, the interest of the fractional order calculation and its applications in various areas such as economy [11], dielectric polarization [15], electromagnetic systems [8] and control theory. The notion of stability is a central issue of control theory, this has a wide range of definitions in [7]. In that sense, the stability of the whole controlled system has to be examined using the fractional order techniques as well. Stability of Caputo and Riemann-Liouville fractional singular systems remains an open problem. It is hard to compute the derivatives of Lyapunov functions and there often happen impulses in the solutions. As long as at present, designing observers for fractional-order systems has not been sufficiently tackled in the bibliography. For example, the lecturer can refer to [13] of observer design for fractional-order linear systems. There are also some works related to nonlinear systems, for instance [10]. In [6], the observer design problem for 1 6 Dec 2021 04:08:36 PST 210708-Echi Version 2 - Submitted to Rocky Mountain J. Math.