Dynamic Output Feedback Synthesis with General Frequency Domain Specifications

This paper considers a control synthesis problem for linear systems to meet design specifications given in terms of multiple frequency domain inequalities in (semi)finite ranges. 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 the linearizing change of variables. We provide a qualification for the multiplier basis matrix to yield nonconservative LMI conditions. It is shown that qualified bases can be found for some cases, and that the qualification can be used to find reasonable choices of the basis for other cases. Finally, the synthesis method is applied to a multiple objective control problem for an active magnetic bearing to demonstrate its utility.