On robust stabilization problem of systems with real parametric uncertainties and the gain margin optimization problem

We consider the robust stabilization problem for a class of uncertain systems with real uncertain parameters. That is, based on the gain margin optimization problem, we demonstrate the importance of the modeling in the application of H^∞ type solution to robust stabilization problem for the real uncertainty case. We show that the modeling technique of choosing the so-called center of a family of plants as the nominal plant and creating a symmetric uncertainty around the nominal portion, which is the usual case with complex uncertainty, results in a conservative solution for the case of real uncertainty. Whereas, a careful modeling, namely using a so-called “auxiliary plant family” allows us to have a nonconservative solution