Robust stabilizing regions of fractional-order PDμ controllers of time-delay fractional-order systems

• The existence conditions and computing methods of RRB curves, CRB curves are investigated.
• The robust stabilizing regions with stability degrees are determined for time-delay fractional-order systems.
• The filers are adopted in controllers, the corresponding stabilizing regions are discussed.

This study investigates the robust stabilizing regions with stability degrees of fractional-order PDμ controllers for time-delay fractional-order systems. By the D-decomposition technology, we identify the stabilizing regions by three types of curves, i.e., the real root boundary (RRB) curves, complex root boundary (CRB) curves and infinite root boundary (IRB) lines. The existence conditions and computing methods of RRB curves, CRB curves and IRB lines are proposed to determine the boundaries of the potential stabilizing regions. The Test Lines and the principle of the identifying the stabilizing regions are presented to find the real stabilizing regions with a given stability degree. To deal with noises existing in the feedback signals, fractional-order PDμ controllers involving filers are adopted. Meanwhile, the robust stabilizing regions are also analyzed via IRB curves, CRB curves and IRB lines with stability degrees. Finally, some illustrative examples are offered to verify the effectiveness of depicting algorithms of the robust stabilizing regions for PDμ controllers with no filer or filers, respectively.