Simultaneous stabilization and existence conditions of robust controller

The existing condition of controller, which can stabilize plant family with parameter uncertainties, and its design approach are considered from the point of set. For designing controller stabilizing a given plant family, a reversing method is adopted by using the concept of value set and the result of Youla. The sufficient condition of existing controller stabilizing the given plant family is given. Under strongly constraint condition, the sufficient and necessary condition is obtained. At last, the design method of controller is provided.