Control Design for Fractional Order Leader and Follower Systems with Mixed Time Delays: A Resilience-Based Approach

Abstract

In this article, we consider the problem of resilient base containment control for fractional-order multi-agent systems (FOMASs) with mixed time delays using a reliable and simple approach, where the communication topology among followers is a weighted digraph. A disturbance term is introduced into the delayed and non-delayed controller part to make it more practical. Our method involves proposing algebraic criteria by utilizing non-delayed and delayed protocols, applying the Razumikhin technique and graph theory respectively. The presented method can well overcome the difficulty resulting from fractional calculus, time delays and fractional derivatives. To demonstrate the validity and effectiveness of our findings, we provide an example at the end of our study.