Order-Dependent Sampling Control of Uncertain FO Linear System

Abstract

This paper proposes a sampled-data control problem for the fractional-order system with parameter uncertainties. First, according to the input delay approach, the dynamics of the considered fractional-order system is modeled by a delay system. The main purpose of the problem addressed is to design a sampled-data controller, such that the closed-loop fractional-order system guarantees the asymptotic stability. Then, the Lyapunov-Krasovskii functional is constructed to derive the stable criterion. The new delay-dependent and order-dependent stability conditions are presented in the form of linear matrix inequalities. Eventually, a new sampled-data controller is designed to ensure the stability and stabilization of fractional-order system. Finally, a numerical example is given to illustrate the effectiveness and superiority of the derived criterion.