Adaptive-sliding mode control of fractional order nonlinear polytopic differential inclusions

In this paper the adaptive-sliding mode control method is generalized to steer state variables of a wide class of fractional order nonlinear polytopic differential inclusions toward a desired fixed point considering unknown bounded disturbance. The proposed fractional order sliding surfaces and designed adaptation laws are employed to generate adaptive-sliding mode control inputs. The stability of the fractional order polytopic differential inclusion with designed control inputs is proved based on the Lyapunov stability theorem. A numerical example and its simulation results are provided to verify that the proposed control input can lead state variables of the aforementioned differential inclusion to desired fixed point.