Hierarchical optimisation in /spl Hscr//sub /spl infin//

In this paper an hierarchical optimal central problem is considered, which involves an /spl Hscr//sub /spl infin// cost in the primary problem and an /spl Hscr//sub /spl infin//-norm type or a quadratic secondary objective. Using an allpass dilation technique and results from superoptimal interpolation theory, it is shown that the problem can be reduced to a multi-disk minimisation in terms of a free parameter of reduced dimensions. At this stage, convex programming techniques may be employed to obtain a numerical solution to the problem.