Lyapunov characterization of the fractional nonlinear systems with exogenous input

Abstract

This paper deals with a Lyapunov characterization of the conditional Mittag-Leffler stability and conditional asymptotic stability of the fractional nonlinear systems with exogenous input. A particular class of the fractional nonlinear systems is studied. The paper contributes to giving in particular the Lyapunov characterization of fractional linear systems and fractional bilinear systems with exogenous input.