A numerical solution to the matrix ℋ2/ℋ∞ optimal control problem

In this paper a numerical solution is obtained to the problem of minimizing an ℋ2-type cost subject to an ℋ∞-norm constraint. The method employed is based on the convex alternating projection algorithm and generalizes a recent technique to the multivariable case. The solution is derived in terms of the Markov parameters of an FIR filter of arbitrary length; this is finally approximated by a low-order IIR filter using Hankel-norm model-reduction techniques. The results are illustrated with a numerical example. © 1997 John Wiley & Sons, Ltd.