Multiobjective H2/H∞ by Banach space operator theory

In this paper Banach space duality theory and operator theory are combined to show that the op- timal performance index in the multiobjective H2/Hm is equal to the operator induced norm of a particu- lar operator. This operator is shown to act on special Banach spaces, and is a projection of a multiplication operator. Finally, under a certain continuity assump- tion, it is shown that there exist maximal vectors, which leads to an exact solution to the multiobjective H2/Hm problem.