Dual Problem in Multi-Objective H Control

In this paper, we approach a multi-objectiveH problem with several H 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 finitedimensional 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 mixedobjective approach.