Stability Testing Set for a Diamond-Type Family of Commensurate Fractional Order Polynomials

This paper deals with robust stability of a diamond-type of commensurate fractional order polynomials. The diamond-type of commensurate fractional order polynomials means the uncertain commensurate fractional order polynomials of which coefficients lie in a diamond type of boxes. In this paper, we show that robust stability of a diamond-type of the commensurate fractional order polynomials is robustly stable if and only if some set of edges of the commensurate fractional order polynomial is robustly stable. The problem of robust stability of a diamond-type of commensurate fractional order polynomials can be changed to the problem about the zero exclusion principle for its value set