Robust Stabilizing Regions of Fractional-order PI^λ Controllers for Fractional-order Systems with Time-delays

This study focuses on a graphical approach to determine the robust stabilizing regions of fractional-order PI^λ(proportional integration) controllers for fractional-order systems with time-delays. By D-decomposition technique, the existence conditions and calculating method of the real root boundary (RRB) curves, complex root boundary (CRB) curves and infinite root boundary (IRB) lines are investigated for a given stability degree. The robust stabilizing regions in terms of the RRB curves, CRB curves and IRB lines are identified by the proposed criteria in this paper. Finally, two illustrative examples are given to verify the effectiveness of this graphical approach for different stability degrees.