Norelys Aguila-Camacho

TL;DR: A new lemma for the Caputo fractional derivatives, when 0 α 1 , is proposed, which has proved to be useful in order to apply the fractional-order extension of Lyapunov direct method, to demonstrate the stability of many fractional order systems, which can be nonlinear and time varying.

TL;DR: The paper presents two new lemmas related to the Caputo fractional derivatives and a theorem for proving uniform stability in the sense of Lyapunov for fractional order systems and is applied to the stability analysis of two Fractional Order Model Reference Adaptive Control schemes.

TL;DR: Comparisons were made among the four FOMRAC designs, a fractional order PID, a classical PID, and four Integer Order Model Reference Adaptive Controllers, showing that the FomRAC can improve the controlled system behavior and its robustness with respect to model uncertainties.

TL;DR: Barbalat-like lemmas for fractional order integrals are presented, which can be used to conclude about the convergence of a function to zero, based on some conditions upon its fractional integral.

TL;DR: The boundedness of the solutions is proved for all three cases, and the convergence to zero of the mean value of one of the variables is also proved.