A behavioral approach to $H_2$ optimal control

In this paper we consider a formulation oftl~ H2 optimal control problem in which the controller is not viewed as an operator that transforms measurements to controls. Instead, the controller is assumed to be a device that constrains a set of a-priori specified interconnection variables so as to achieve a controlled system whose manifest vari~ - ave a free component and satisfy an upperbound on th £2 norm of its impulse response. We formalize and solve this problem in a behavioral setting, that is, without reference to system representa nd input-output structures. TI ivalance between th H2 control problem, the generalize H2 control problem and the LQ optimal control problem are established.