Robust asymptotic stability of interval fractional-order nonlinear systems with time-delay

This paper studies the global asymptotic stability of a class of interval fractional-order (FO) nonlinear systems with time-delay. First, a new lemma for the Caputo fractional derivative is presented. It extends the FO Lyapunov direct method allowing the stability analysis and synthesis of FO nonlinear systems with time-delay. Second, by employing FO Razumikhin theorem, a new delay-independent stability criterion, in the form of linear matrix inequality is established for ensuring that a system is globally asymptotically stable. It is shown that the new criterion is simple, easy to use and valid for the FO or integer-order interval neural networks with time-delay. Finally, the feasibility and effectiveness of the proposed scheme are tested with a numerical example.