On some approaches to the simultaneous stabilization of linear plants by a controller of a given structure

In the present paper, we consider the problem of simultaneous stabilization of linear scalar stationary plants of arbitrary order for which we obtain numerically verifiable necessary conditions for simultaneous stabilization and a sufficient condition with the indication of a constructive algorithm for synthesizing a stabilizing controller. We also consider the problem of extending the set of simultaneously stabilized plants. For the solution of these problems, we use an approach based on the analysis of the structure of stability domains in the spaces of coefficients of polynomials linearly depending on parameters.