Finite time stability and sliding mode control for uncertain variable fractional order nonlinear systems

Abstract

Abstract This paper deals with the finite time stability and control for a class of uncertain variable fractional order nonlinear systems. The variable fractional Lyapunov direct method is developed to provide the basis for the stability proof of the system considered. The sliding mode control method is applied for robust control of uncertain variable fractional order systems; furthermore, the chattering phenomenon is avoided. And the finite time stability of the systems under control law is proved based on the proposed stability criterion. Finally, numerical simulations are proposed and the efficiency of the controller is verified.

Keywords

• Uncertain variable fractional order system
• Finite time stability
• Robust control
• Sliding mode control method