Stabilization via static output feedback

Necessary and sufficient conditions for the existence of stabilizing static output feedback gains are presented. The requirement of output feedback introduces a structural constraint between the states and the controls. It is shown that such a structural constraint is satisfied if and only if the weighting matrix associated to the cross term of the quadratic loss function satisfies some conditions. The authors demonstrate that any stabilizing static output feedback is the solution of a linear quadratic control problem where the cost function has a suitable cross term