Continuous finite-time stabilization for some classes of fractional order dynamics

This paper analyzes some basic issues involving the application of discontinuous control techniques for controlling fractional order systems (FOS). With reference to a simple class of SISO perturbed processes, we compare the performance of two distinct approaches, namely the “fractional sliding manifold” (FSM) approach, and the “fractional dynamic input extension” (FDIE) approach. The latter, which is the main new contribution of this paper, is shown to provide for the finite time convergence property of the systems' state. Remarkably, this approach also attenuates the chattering phenomenon by leading to a continuous, although obviously non-smooth, control action. The performance of the two methodologies under investigation are determined by means of Lyapunov approach. Additionally, we derive two new results involving the application of second-order sliding mode control techniques in the context of SISO FOS, and the application of the unit-vector methodology for controlling uncertain multivariable FOS. The presented analysis is supported by simulation results.