American Journal of Mathematics and Statistics 2014, 4(5): 222-230 DOI: 10.5923/j.ajms.20140405.03 Robust Asymptotically Stabilization of Special Uncertain Descriptor Fractional-Order Systems with Fractional Feedback Control Sameer Qasim Hasan * , Ala Muhsien Abd Department of Mathematics, Almustansiriyah University, Baghdad, Iraq Abstract In this paper we investigate the asymptotically stabilization of a special type of singular fractional order α belongs to interval (0,1) with uncertain parameter as time-invariant and norm-bounded appearing in the state matrix and suitable feedback fractional control by using Dynamics decomposition form. Keywords Fractional order, Descriptor system, Fractional, System, Fractional control, Feedback control 1. Introduction Recently, fractional-order control systems have attracted increasing interest [15, 9, 11]. On the one hand, this is mainly due to the fact that many real-world physical systems are well characterized by fractional-order state equations [15], i.e., equations involving the so-called fractional derivatives and integrals. On the other hand, with the success in the synthesis of real noninteger differentiators and the emergence of a new electrical circuit element called “fractance” [10, 21], fractional-order controllers [16, 18, 12] have been designed and applied to control a variety of dynamical processes, including integer-order and fractional-order systems, so as to enhance the robustness and performance of the control systems. Singular fractional systems (known as generalized, descriptor of Fractional systems) describe a large class of systems, which are not only theoretical interest but also have a great importance in practice. Stability is fundamental to all control systems, certainly including fractional-order control systems [20, 19]. Recently, stability and stabilization problems of fractional-order linear time-invariant interval systems have been investigated in [1], [2, 4]. For example, for fractional-order linear time-invariant interval systems described in the transfer function form, the stability issue was discussed first in [13] and then further in [14]. In this paper we consider the problem of the robust asymptotical Stabilization for uncertain descriptor fractional-order systems. * Corresponding author: dr.sameer_kasim@yahoo.com (Sameer Qasim Hasan) Published online at http://journal.sapub.org/ajms Copyright © 2014 Scientific & Academic Publishing. All Rights Reserved The descriptor multi-fractional-order systems by applying a derivative multi-controller and a state feedback. Controller is given to achieve the robust asymptotical stabilization of the obtained two sub system, first is fractional-order systems and the second is zero state. We using canonical form for the descriptor fractional-order systems and by applying a derivative controller and a state feedback controller is given to achieve the robust asymptotical stabilization of the fractional-order systems. In section II, the paper are organized as follow in section II, we introduce the definition of fractional derivative in brief; we present also some mathematical results. In section III, we propose robust linear uncertainty descriptor multi-fractional controller for the stabilization of system. 2. Preliminaries A. Some definition Now we review some important and definition: The Caputo derivative on the other, defined [17], α t α α α-n+1 a d f(t) 1 dt D f(t) = dτ Γ(n - α) (t - τ) ∫ , ( 1 ) n n α − ≤ < For ( 1 ) n n α − ≤ < and Γ(x) is the well-known Euler’s gamma function. Definition (2.1), [22]: Let [ ] m n ij A aB × = ∈  , pq B × ∈  . Their Kronecker product (i.e., the direct product or tensor product), denoted as ( ) A B ⊗ , is defined by