Fractional‐order controllers for irrational systems

In this contribution, fractional-order controllers of the type PDμ and PIλ are applied to a class irrational transfer function models that appear in large-scale systems, such as networks mechanical/electrical elements distributed parameter systems. More precisely, by considering controller k p + η s α Laplace domain with − 1 ≤ , stability analysis parameter-space ( ) is presented. Furthermore, way measure robustness, controller's fragility using derived. Finally, several applications demonstrate utility our results included.