Fractional order stability of systems

This paper investigates and offers some stability analysis methods for systems of non-integer orders. Well known analysis methods such as Hurwitz, interlacing property, monotonic phase increment property are reconsidered in a fractional order way of thinking. A method to find the roots of the so-called fractional order polynomials is proposed and Hurwitz-like stability of the pseudo-polynomials is investigated. Effectiveness of the interlacing property and outcomes of the monotonic phase increment property for fractional order case is shown. Results are comparatively proved and illustrated clearly.