Complex polytopic control Lyapunov functions

In this paper, the class of real Lyapunov functions induced by complex polytopes is investigated. Such polytopes are in some sense the extension of real polytopes to the complex space, but have some peculiar aspects which might be relevant for the solution of constrained and/or robust control problems. In detail, analysis and synthesis results (which rely on real polytopes) for a class of linear uncertain systems are extended to the complex case. A relevant contribution of this new extensions is that of showing that the stabilizability (stability) conditions imply that the projection (projection and intersection) on the real space of such complex polytopes are level sets of control Lyapunov functions, say they can be used to derive a stabilizing control law