Finite-Time Stabilization of Fractional Order Uncertain Chain of Integrator: An Integral Sliding Mode Approach

Abstract

In this technical note, a novel methodology for robust finite-time stabilization of a chain of uncertain fractional order integrator is proposed. This is achieved by first designing a nominal controller which stabilizes the system in finite time. An integral sliding-mode like surface and a switching controller is proposed such that when the system is on the surface the equivalent value of the integral sliding-mode control is the negative of the disturbance and hence the disturbance is cancelled. An improved strategy with more general kind of uncertainty is also proposed. Numerical examples are presented to illustrate the proposed methods.