MIMO optimal control design: the interplay of the /spl Hscr//sub 2/ and the l/sub 1/ norms

We consider the problem of minimizing the /spl Hscr//sub 2/ performance of the closed loop subject to a l/sub 1/ constraint. The development is devoted to multi-input multi-output (MIMO) systems. It is shown that approximating solutions to the optimal within any a priori given tolerance can be obtained via a finite dimensional quadratic optimization problem whose dimension is known a priori.