  An easy-to-use and effective formula for stability testing of a system with
fractional-delay characteristic equation in the general form of
$\Delta(s)=P_0(s)+\sum_{i=1}^N P_i(s)\exp(-\zeta_i s^{\beta_i}) =0$, where
$P_i(s)$ ($i=0,..., N$) are the so-called fractional-order polynomials and
$\zeta_i$ and $\beta_i$ are positive real constants, is proposed in this paper.
The proposed formula determines the number of unstable roots of the
characteristic equation (i.e., those located in the right half-plane of the
first Riemann sheet) by applying Rouche's theorem. Numerical simulations are
also presented to confirm the efficiency of the proposed formula.
