H∞-optimal feedback controllers for linear multivariable systems

This paper treats the problem of designing, for a linear multivariable plant, a feedback controller which minimizes the
H^{\infty}
-norm of a weighted sensitivity matrix. There exists a family of optimal improper feedbacks. This family is determined by application of a theory of Ball and Helton. A method for computing optimal feedbacks is described in detail and a numerical example is included. It is shown that an optimal improper feedback can be approximated by a proper one under certain conditions on the weighting matrices.