Design of a robust controller for a plant family

Problem of simultaneous stabilization of a plant family is studied. A controller including a parameter is designed to stabilize simultaneously two specified plants of which one is a nominal plant while the other a "worst point" plant. The basic idea is to find the two specified plants and use them to design a robust controller including the parameter. Since the parameter is introduced, the robust controller can be designed using existence methods. The parameter in the controller can be obtained using the theory of stability of plant family system. Hence, the problem of designing a controller is converted into the problem of checking the stability. The controller can be designed by simultaneously stabilizing the plant family and determining the parameter in the "worst point" plant.