Exact Certificates for Strong Stabilization via Numerical Algebraic Geometry

Aim of this letter is to apply numerical algebraic geometry to the strong stabilization problem with fixed structure controllers. Using as a working example a plant taken from the literature and a dynamic controller with two parameters, it is shown how a combination of numerical and symbolic algorithms can be used to “exactly certify” whether a solution exists or not in a bounded range of parameters, and, when the problem is solvable, to provide one solution. The theory is illustrated in detail for the working example, but the results are given for the general case and the effectiveness of the method is further tested on four additional benchmark examples.