MIMO OPTIMAL-CONTROL DESIGN - THE INTERPLAY BETWEEN THE H-2 AND THE L(1) NORMS

In this paper we consider controller design methods which can address directly the interplay between the H-2 and l(1) performance of the clo sed loop. The development is devoted to multi-input/multi-output (MIMO ) systems. Two relevant multiobjective performance problems are consid ered each being of interest in its own right. In the first, termed as the combination problem, a weighted sum of the l(1) norms and the squa re of the H-2 norms of a given set of input-output transfer functions constituting the closed loop is minimized. It is shown that, in the on e-block case, the solution can be obtained via a finite-dimensional qu adratic optimization problem which has an a priori known dimension. In the four-block case, a method of computing approximate solutions with in any a priori given tolerance is provided. In the second, termed as the mixed problem, the H-2 performance of the closed loop is minimized subject to an l(1) constraint. It is shown that approximating solutio ns within any a priori given tolerance can be obtained via the solutio n to a related combination problem.