Robust stabilization criterion of fractional-order controllers for interval fractional-order plants

The robust stabilization criterion of fractional-order controllers for interval fractional-order plants is proposed in this study. For the interval uncertainties existing in the numerator and denominator of a transfer function with respect to a fractional-order plant, the vertices of the value set corresponding to the characteristic function are offered by the Minkowski Sum. This algorithm for getting the vertices avoids to calculate the redundant vertices, reducing the computational complexity. An auxiliary function reflecting the position relationship between the origin and the value set is defined to investigate the robust stability conditions. The lower and upper limits of the test frequency interval are offered to check the auxiliary function within a finite frequency. Supposing that the fractional-order controller can stabilize the nominal fractional-order plant, the stabilization criterion of the closed loop system with interval uncertainties is provided based on the auxiliary function and other two conditions. Finally, three illustrative examples with fractional-order controllers are given to validate the effectiveness of this robust stabilization criterion.