A Nyquist-like approach for stability analysis in fractional-order systems: Related issues and case Studies

In this note, we consider a Nyquist-like criterion for stability analysis in linear dynamical systems that are described by fractional-order linear time-invariant (FOLTI) differential equations, associated with commensurate-order characteristic polynomials, by means of the argument principle. Based on some appropriately chosen integral contour for applying the argument principle, the stability conditions are necessary and sufficient, independent of zeros/poles distribution, which can be implemented as we do in using general Nyquist-like criteria graphically. Contour detouring and locus discontinuity are examined. Existing numerical examples are re-visited as case studies.