Abstract: For systems with ellipsoidal parametric uncertainty,an condition for robust state feedback control is proposed by means of linear matrix inequality principle.The condition takes the form of a linear matrix inequality.When this condition is satisfied,the robust state feedback gain matrix can be easily derived to guarantee robust stability and prescribed closed-loop performance.Based on prediction error identification,the estimate values of the unknown parameters are derived using input-output measurement datas.The positive answer to robust control and parameter identification can be obtained from the semidefinite program.Finally the efficiency of this method is illustrated with a simulation example.