Robust Stability Region of Fractional Order Interval Plant with Time Delay

The paper presents a method to compute the robust stability region of fractional order interval plant with time delay by using fractional order PIλDμ controller. The edge theorem is adopted to decompose interval plant to several vertices sub-plants. The characteristic polynomials of vertices sub-plants and the value set of exposed edge for polytope are given. The D-decomposition technique is applied to solve the stability region of each vertices sub-pant. The values of λ and μ of PIλD and PIDμ controllers are obtained in the biggest stability region of all sub-plants. The fraction order PIλDμ controller is constructed by the values of λ and μ. The stability region of each sub-plant is plotted by using fractional order PIλDμ controller. Furthermore, the overlap of stability region of each sub-plant is the stability region of fractional order interval plant with time delay. The paper also proves that the overlap of stability region is the robust stability region of fraction order interval plant.