Finite-time Stability Analysis of Fractional-order with Multi-state Time Delay
In this paper, the finite-time stabilization of a class of multi-state time delay of fractional-order system is proposed. First, we define finite-time stability with the fractional-order system. Second, by using Generalized Gronwall's approach and the methods of the inequality, we get some conditions of finite-time stability for the fractional system with multi-state delay. Finally, a numerical example is given to illustrate the result.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1330715Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1586
 Domenico Delbosco, Luigi Rodino, Existence and uniqueness for a nonlinear fractional di?erential equation, J. Math. Anal. Appl. 204(1996)609-625.
 Xiuyun Zhang, Some results of linear fractional order time-delay system, Appl. Math. Comput.197 (2008)407-411.
 Richard J-P. Time delay systems: An overview of some recent advances and open problems. Automatica 2003; 39: 1667-94.
 M. Zavarei, M. Jamshidi, Time-Delay Systems: Analysis, Optimization and Applications, North-Holland, Amsterdam, 1987.
 M. P. Lazarevi'c,Finite time stability analysis of fractional control of robotic time-delay systems, Mech.Res. Comm. 33(2006)269-279.
 Mihailo P. Lazarevi'c, Aleksandar M. Spasi? b, Finite-time stability analysis of fractional order time-delay systems: Gronwall-s approach, Mathematical and Computer Modelling 49(2009)475-481.
 Kilbas A-A, Srivastava H-M, Trujillo J-J. Theory and applications of fractional differential equations.Mathematics studies204. Elsevier, North-Holland2006.
 Oldham KB, Spanier J.The Fractional Calculus.New York: Academic Press; 1974.
 H.Ye, J. Gao, Y.Ding, Ageneralized Gronwall inequality and its application to afractional differential equation, J.Math. Anal.Appl.328 (2007)1075-1081.