A convex programming approach to the multiobjective H2/H∞ problem

In this paper, Banach space duality theory for the multiobjective H²/H^∞ problem developed recently by the authors, is used to develop algorithms to solve this problem by approximately reducing the dual and predual representations to finite variable convex optimizations. The Ellipsoid algorithm is then applied to these problems to obtain polynomial-time, nonheuristic programs which find "nearly" optimal control laws. These algorithms have been implemented numerically to compute an example.