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

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 previous results in the specialized literature, including those of Cong et al. We use the proposed theorems in adaptive systems, proving convergence and robustness of such schemes, that up to date remain unsolved problems, showing the wide scope of application of our results.