Abstract
In this paper, an optimal solution of the continuous-time L1 control problem for 1-block MIMO systems is studied. Firstly, a characterization of an optimal solution is derived. A crucial idea of the approach is the duality of convex sets of finite dimensional vector spaces. This avoids a functional space argument. Secondly, it is shown that confining controllers to be finite dimensional does not hamper the ablitity to reduce the L∞ induced norm of the closed loop operator.
