On a H2-optimization problem under asymptotic tracking and decoupling constraints

In this paper, a servomechanism problem is considered in which a stabilizing controller is to be chosen as the solution of a H₂-optimization problem with asymptotic tracking and (exact or approximate) decoupling constraints. An explicit parametrization is presented of all controllers which ensure asymptotic tracking (of a class of persistent signals) and satisfy the exact decoupling constraint, on the basis of which the optimization problem in question is re-posed as an unconstrained problem. Two versions of the approximate decoupling constraint are considered which lead to H₂-problems with, respectively one or several H₂constraints. The effect on the attained optimal cost value of the exact and approximate decoupling constraints is illustrated in a numerical example.