In this paper, a servomechanism problem is considered in which a stabilizing controller is to be chosen as the solution of a H{sub}2-optimization problem with asymptotic tracking and (exact or approximate) decoupling constraints. The cost functional is made-up of terms which penalize the tracking error and control effort associated with a class of persistent reference signals. To solve the optimization problem with asymptotic tracking and exact decoupling constraints, an explicit parametrization is presented of all stabilizing controllers which satisfy these constraints. On the basis of this parametrization the problem in question is recast as an unconstrained H{sub}2 problem and conditions on problem data are then stated under which there exists a unique solution. To handle the case of asymptotic tracking and approximate decoupling constraints, a parametrization of all stabilizing controllers which achieve asymptotic tracking is used to eliminate the tracking constraint; this leads to an H{sub}2 optimization problem with several non-definite H{sub}2 constraints. Approximate solutions to such a problem are obtained by means of a sequence of H{sub}2 problems with a single non-definite H{sub}2 constrain which, in turn, are solved by line search and spectral factorization. A numerical example is presented to illustrate the effect of the exact and approximate decoupling constrains on the attained optimal cost value and time responses.
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