Dual problem in multi-objective Hp control

In this paper, we approach a multi-objective H^p problem with several H^p constraints from the Banach duality point of view. The problem is reduced to an abstract norm minimization problem, and the dual problem is derived using the classical Banach result. It completes the primal-dual pair which can be used to solve the problem numerically by finite-dimensional approximations. While the approximation of the primal problem gives an upper bound of the optimal value, the approximation of the dual problem provides a lower bound, and the gap between them can be done arbitrary small. In view of growing computational power of modern computers, it gives a good alternative to the standard mixed-objective approach.