The output feedback control proposed until now is added to system noise and when observing an output, the probable outputfeedback control in consideration of the output observation noise mixed in an observation process is proposed. Although thisproposing method assumes the actual system since only state is treated as a cost function There is a problem of being hard toapply to the actual control problem which has a limitation in the control input. Then, system noise and output observation no ise istaken into consideration, Let quadratic of output power, and quadratic of control input be a cost function, The control problemwhich asks for the output feedback gain which minimizes this cost function is proposed. As opposed to such a control problem,we show the solvability conditions.
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