Robust stabilization of interval fractional-order plants with one time-delay by fractional-order controllers

Abstract

This study investigates the robust stabilization of interval fractional-order plants with one time-delay using fractional-order controllers by the Minkowski sum of value sets. The characteristic function of a closed loop system in terms of the fractional-order controller and an interval fractional-order plant with one time-delay is divided into the nominal function and disturbance function. By the Minkowski sum, the value set of disturbance function is obtained to avoid the calculation for the redundant vertices. Based on the zero exclusion principle, the robust stabilization conditions are provided. The computing method of the upper and lower limits of a finite frequency interval is offered to achieve the test operation of the robust stabilization criterion. Under the assumption that the fractional-order controller can stabilize the nominal plant, three conditions in the proposed theorem ensure that the corresponding fractional-order controller can stabilize the interval fractional-order plant with one time-delay. Finally, two illustrative examples are provided to verify the effectiveness of this proposed robust stabilization criterion.