Inverse problem of a modified LQ control

A frequency-domain characterization of the solution to a modified LQ problem, which have been formulated and solved by the present authors, is discussed. In the modified LQ problem the optimal state feedback law is supposed to be determined in terms of minimum covariance matrix of the state vector. Without costing the control power, the problem is made well-posed by assuming state observation noise that effectively suppresses the control power. An inequality condition similar to the well known circle criterion is derived as a necessary and sufficient condition for a state feedback law to be the solution to some LQ problem of the modified form.