We investigate the linear optimal control problems in the context of dynamic state feedback configuration. The dynamic state feedback is a dual structure of the dynamic observer. In conjunction with the well known arguments on linear matrix differential and Lyapunov equations, we elicit the fact that the quadratic performance index is always computable with this configuration. Based on this property, we suggest a nonlinear optimization programming method to get suboptimal or near optimal time-invariant dynamic state feedback controls. One can also evaluate the efficacy of pre-designed dynamic state feedback controllers utilizing this property. Two illustrative examples are given to show the effectiveness of the proposed approach.