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Abstract This paper considers a control synthesis problem for linear systems to meet design specifications in terms of multiple frequency domain inequalities in (semi)finite ranges. Our approach is based on the generalized Kalman–Yakubovich–Popov (GKYP) lemma, and dynamic output feedback controllers of order equal to the plant are considered. A new multiplier expansion is proposed to convert the synthesis condition to a linear matrix inequality (LMI) condition through a standard linearizing change of variables. In a single objective setting, the LMI condition may or may not be conservative, depending on the choice of the basis for the multiplier expansion. We provide a qualification for the basis matrix to yield non‐conservative LMI conditions. It is difficult to determine the basis matrix meeting such a qualification in general. However, it is shown that qualified bases can be found for some cases, and that the qualification condition can be used to find reasonable choices of the basis for other cases. The synthesis method is then extended to the multiple objective case where a sufficient condition is given for the existence of a controller to meet all the prescribed specifications. Finally, design examples for an active magnetic bearing are given to illustrate the effectiveness of the proposed design method. Copyright © 2006 John Wiley & Sons, Ltd.
Iwasaki et al. (Tue,) studied this question.