Homogeneous Polynomial Forms for Simultaneous Stabilizability of Families of Linear Control Systems: A Tensor Product Approach

This note uses the formalism of tensor products in order to deal with the problem of simultaneous stabilizability of a family of linear control systems by means of Lyapunov functions which are homogeneous polynomial forms. While the feedback synthesis seems to be nonconvex, the simultaneous stability by means of homogeneous polynomial forms of the uncontrollable modes yields (convex) necessary but not sufficient conditions for simultaneous stabilizability.