Robust stabilization of the system family

The problem of robust stabilization of a system family is studied here. A sufficient condition for the existence of a robust controller is presented under the assumption that there are perturbations both in the numerator and in the denominator of the nominal system. This condition can be given by an inequality that is satisfied by the coefficient vectors of the perturbed polynomials. Based on this, the robust controller family stabilizing the system family can be obtained. Therefore, the condition has the advantages of easy computing and further satisfying other required properties.