Stability of fractional-order linear systems can be tested by transfer functions directly.

What is it about?

Stability criteria are claimed via frequency-domian features of fractional order linear time-invariant systems. The critria do not use inter-domain transformation of characteristic polynomials and their pole/eigenvalues. They are utilized graphically with locus plotting or numerically without locus plotting. They can be used in fractional-order systems with multiple fractional calculus, or multivariable in input/output structure.

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Why is it important?

The stability criteria are Nyquist-like ones for fractional-order systems. However, stability conditions are implementable directly and explicitly: 1) there is no need to transfer the fractional-order characteristic polynomials into regular-order ones; 2) no open-loop poles are needed even if the open-loop system is unstable; 3) the criteria can be employed by drawing Nyquist-like locus, or by computing the argument increment numerically.

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