On the optimal two-block H∞ problem

This paper provides the duality structure of the optimal two-block H^∞ problem. The dual description leads naturally to a numerical solution based on convex programming for LTI (including infinite dimensional) systems. Alignment conditions are obtained and show that the optimal solution is flat in general, and unique in the SISO case. It is also proved that under specific conditions, a well-known Hankel-Toeplitz operator achieves its norm on the discrete spectrum, therefore generalizing a similar result obtained formerly for finite-dimensional (rational) systems. The norm of this Hankel-Toeplitz operator corresponds to the optimal two-block H^∞ performance.