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

TL;DR

This paper establishes new sufficient conditions for robustness and convergence in linear time-varying fractional systems, and demonstrates their application in adaptive systems, addressing previously unresolved problems.

Contribution

It generalizes existing results on fractional systems' robustness and convergence, and applies these to solve open problems in adaptive system stability.

Findings

Theorems that extend previous results on fractional systems.

Proven convergence of adaptive schemes using the new theorems.

Demonstrated robustness of fractional systems under new conditions.

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.