On the order of optimal controllers in the mixed H-2/H-infinity control

摘要

It is shown that the so-called "pure" mixed H/sub 2//H/sub /spl infin// optimization problem does not have a "good" solution. More precisely, a class of nonsingular "pure" mixed H/sub 2//H/sub /spl infin// optimization problems (minimization of an L/sub 2/-norm subject to a Youla parameterization and an L/sub /spl infin// constraint) is considered. It is shown that, whenever the L/sub /spl infin// constraint is not redundant, the optimal controller has infinite order, and does not allow exponentially stable state space realization.