Robustness and convergence of fractional systems and their applications to adaptive schemes

Abstract

Our general aim is to give sufficient conditions for robustness behavior and convergence to the equilibrium point of linear time-varying fractional system's solutions. We approach this problem using as a framework a series of recent results due to Cong et al. We establish theorems that generalize in several ways many previously published results, including those of Cong et al. We use the proposed theorems in control and adaptive systems, proving convergence and robustness of such schemes, that up to date remain as unsolved problems, showing the wide scope of applications of our results.