COMPUTATIONAL COMPLEXITY OF A PROBLEM ARISING IN FIXED ORDER OUTPUT FEEDBACK DESIGN

摘要

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-infinity control, guaranteed H-2 control, and mixed H-2/H-infinity, 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. (C) 1997 Elsevier Science B.V. [References: 12]