Optimal H/sub 2//l/sub 1/ control via duality theory

In this paper we consider the problem of minimizing the H/sub 2/-norm of the closed-loop map while maintaining its l/sub 1/-norm at a prescribed level. The problem is analyzed in the case of discrete-time, SISO closed-loop maps. Utilizing duality theory, it is shown that the optimal solution is unique, and, in the nontrivial case where the l/sub 1/ constraint is active, the optimal solution has a finite impulse response. A finite step procedure is given for the construction of the exact solution. This procedure consists of solving a finite number of quadratic programming problems which can be performed using standard methods. Finally, continuity properties of the optimal solution with respect to changes in the l/sub 1/-constraint are established.<
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