Loopshaping by quadratic constraints on open-loop transfer functions

The purpose of this note is to propose to execute loopshaping by imposing q uadratic constraints on open-loop transfer functions. Quadratic constraints are defined to be consistent with feedback stable systems. Then, a robust stability analysis and a loopshaping; method under quadratic constraints on open-loop transfer functions are given. Our results provide a general robu stness of feedback systems in terms of open-loop transfer functions, includ ing robustness based on gain and phase margins.