Strengthened H∞ control via state feedback: a majorization approach using algebraic Riccati inequalities

We extend the algebraic Riccati equation approach to H^∞/H² state-feedback design to incorporate additional constraints on the other (nonmaximum) singular values. It is shown that a state-feedback control law that satisfies a singular-values/singular-vectors constraint exists if and only if a corresponding algebraic Riccati inequality admits a stabilizing and positive-definite solution. The results are applied to devise a majorization approach for constructing state-feedback controllers that strive to optimize some obvious design objectives.