A note on stability robustness computation

Stability robustness computations for polynomials with coefficients which are affine functions of perturbations are presented. In the case when the perturbation is of a delay type, a necessary and sufficient condition for use in stability testing independent of delay is given. The authors then discuss whether a given polynomial of this kind is stable (all roots are in the open left half plane) without delays. As an application, the formula derived for polynomials can be used to calculate the delay margin for a control system since the calculation of delay margin in control theory can be converted to the calculation of the stability margins of polynomials as defined in the paper. Based on a similar idea, it is possible to calculate gain and phase margins as well as a combined gain and phase margin. Therefore, the proposed approach provides a unified way of calculating gain and/or phase and delay stability margins