Multi-objective MIMO optimal control design without zero interpolation

An optimal controller design which addresses the concerns of the H ₂ and the l₁ norms is studied. In the first problem a positive combination of the H₂ and the l₁ norms of the closed loop is minimized. In the second the l ₁ norm of a transfer function is minimized while restraining the another below a prespecified level. Converging upper and lower bounds are obtained. Relation to the pure l₁ problem is established. The solution methodology does not involve zero interpolation to characterize the achievable closed-loop maps. Thus obtaining the controller from the optimal closed-loop map is very straightforward