Robust stabilization of a class of three-dimensional uncertain fractional-order non-autonomous systems

Subject Areas : International Journal of Industrial Mathematics

A. R. Haghighi ¹ , M. Pourmahmood Aghababa ² , M. Roohi ³

1 - Department of Mathematic, Urmia University of Technology, Urmia, Iran
2 - Electrical Engineering Department, Urmia University of Technology, Urmia, Iran
3 - Department of Mathematic, Urmia University of Technology, Urmia, Iran

Received: 2014-02-06 Accepted : 2014-02-06 Published : 2014-04-01

Keywords: Control, Single control input, Fractional-order systems,

Abstract :

This paper concerns the problem of robust stabilization of uncertain fractional-order non-autonomous systems. In this regard, a single input active control approach is proposed for control and stabilization of three-dimensional uncertain fractional-order systems. The robust controller is designed on the basis of fractional Lyapunov stability theory. Furthermore, the effects of model uncertainties are fully taken into account. Also, the robust stability and access to the equilibrium point of the control scheme are analytically proved. Moreover, fast response and easy realization in real world applications are somespecial features of the suggested method. Finally, as a numerical simulation, control and stabilization of three-dimensional uncertain fractional-order Chen system is provided to illustrate the usefulness and applicability of the proposed approach in practice. It is worth to notice that the proposed active control approach can be employed for robust stabilization of a large class of three-dimensional uncertain nonlinear fractional-order non autonomous dynamical systems.