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

It is shown that the so-called “pure” mixed H₂ /H_∞ optimization problem does not have a “good” solution. More precisely, a class of nonsingular “pure” mixed H₂/H_∞ optimization problems (minimization of an L₂-norm subject to a Youla parameterization and an L_∞ constraint) is considered. It is shown that, whenever the L_∞ constraint is not redundant, the optimal controller has infinite order, and does not allow exponentially stable state space realization