Abstract
This paper is concerned with a matrix inequality problem which arises in fixed order output feedback control design. This problem involves finding two symmetric and positive definitive matrices X and Y such that each satisfies a linear matrix inequality and that XY= I. It is well-known that many control problems such as fixed order output feedback stabilization, H ∞ control, guaranteed H 2 control, and mixed H 2/ H ∞ control can all be converted into the matrix inequality problem above, including static output feedback problems as a special case. We show, however, that this matrix inequality problem is NP-hard.
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