An algebraic approach to robust H ∞ control via state feedback

Abstract This paper considers the problem of robust H ∞ control design for linear uncertain systems. We show that for a certain type of time-varying norm-bounded parameter uncertainty, the problem is equivalent to an H ∞ control problem. Therefore, a complete solution is achieved by using the existing results of H ∞ control theory. The paper presents a state feedback design which stabilizes the plant for all admissible uncertainties and also guarantees a prescribed level of disturbance attenuation in a certain sense.