Optimal robust disturbance attenuation for MIMO uncertain systems in H∞

We consider the optimal robust disturbance attenuation problem (ORDAP) for multi-input multi-output (MIMO) uncertain plants. Duality theory is used to show the existence of optimal feedback laws. Next a key multiplication operator acting on particular vector-valued Hardy spaces is introduced. It is then proved that ORDAP for MIMO systems is equal to the operator induced norm of a specific operator. The latter is shown to be a combination of multiplication and Toeplitz operators. An “infinite matrix” representation with respect to a canonical basis is derived, and the norm of the relevant operator is approximated by special matrix norms