Delay-Dependent and Order-Dependent Stability and Stabilization of Fractional-Order Linear Systems With Time-Varying Delay

Abstract

Stability of fractional-order (FO) delayed systems remains a formidable problem. In this brief, asymptotic stability and stabilization of FO linear systems with time-varying structured uncertainties and time-varying delay are discussed. By employing FO Razumikhin theorem, two new delay-dependent and order-dependent stability criteria in form of LMI for FO nominal systems and FO uncertain sytems are first formulated, respectively. Moreover, state feedback controllers of stabilization are also derived with the help of the proposed stability criteria. The numerical simulation demonstrates the effectiveness of the theoretical formulation.