Stability and stabilizability analysis of fractional-order time-varying delay systems via diffusive representation

Abstract

In this work, the stability and stabilization of fractional-order time-varying delay systems modeled in state space are considered. First, based on the indirect Lyapunov and Lyapunov-Krasovskii approaches, we provide a sufficient condition for the asymptotic stability for the fractional-order time-varying delay systems. Then, we give a sufficient condition guaranteeing the existence and the synthesis of pseudo-state feedback stabilizing controller in a Linear Matrix Inequality (LMI) formulation. Finally, a numerical example is given to illustrate the main results.