Robust stability analysis of uncertain incommensurate fractional order quasi- polynomials in the presence of interval fractional orders and interval coefficients

This paper deals with the robust stability analysis of a class of incommensurate fractional order quasi-polynomials with a general type of interval uncertainties. The concept of the general type of interval uncertainties means that all the coefficients and orders of the fractional order quasi-polynomials have interval uncertainties. Generally, the computational complexity of specifying the robust stability of such a quasi-polynomial is shown in this paper. To this end, the robust stability is studied by Principle of Argument theorem. In fact, by presenting two theorems and three lemmas it is shown that the robust stability of a fractional order quasi-polynomial involving the general type of uncertainty can be simply investigated without needing to plot its value set by heavy computations. Examples are attested the validity of the paper results.