Stability of fractional‐order switched non‐linear systems

Abstract

This study addresses the stability issue of a class of fractional-order switched non-linear systems. A general stability condition is established based on which two new concepts named Mittag-Leffler increment and average Mittag-Leffler increment are proposed and two alternative stability conditions are obtained. These conditions fully reveal the trade-off between each subsystem's dynamics, and the value of the fractional order. The new results are further applied to a class of fractional-order multi-agent systems with switching cooperative control laws.