Robust stabilization of commensurate fractional order interval plants with proportional controllers

In this paper, we show that a special class of commensurate fractional order interval plants can be stabilized by proportional compensator if some of extreme plants can be stabilized by the compensator. The special class of commensurate fractional order interval plant means that both its numerator and denominator polynomials has the orders whose values are the multiples of the irrational number between one and two. The proof is based on the fact that the special commensurate fractional order interval polynomial is robustly stable if and only if a small set of vertex polynomials are robustly stable. The special commensurate fractional order interval polynomial has terms whose exponents are the multiples of the irrational number between one and two.