Algorithms for constructing controllers simultaneously stabilizing second-order linear plants

We consider the simultaneous stabilization problem for second-order linear scalar stationary plants and obtain an easy-to-verify necessary condition for simultaneous stabilization as well as a sufficient condition with a constructive algorithm for designing a stabilizing controller. The problem of extending a set of simultaneously stabilizable plants is considered as well. To solve these problems, we use an approach based on the consideration of parametric spaces of polynomials and transfer functions and on a method for finding the stability radii of the polynomials.