Complex stability margin computation based on computer algebra

This paper describes a symbolic method for robust stability analysis of which the stability margin (k_M) problem can be formulated by solving polynomial systems using symbolic computation. Once the solutions are found, the stability margin problem can be easily solved. For the complex k_M problem, no matter how many uncertainties, there is only one polynomial system which needs to be solved in order to find all singularities to determine whether the boundary of Horowitz template intercepts the origin or not. In addition, the corresponding polynomial systems can be transformed into several zero-dimensional polynomial systems which are considered as easy problems by many mathematicians and computer scientists. Therefore, we can compute exact the complex μ efficiently by this method