Static Gain Feedback Control Synthesis with General Frequency Domain Specifications

This paper considers a robust control synthesis problem for uncertain linear systems to meet design specifications given in terms of multiple frequency domain inequalities in (semi)finite ranges. In this paper, we restrict our attention to static (gain feedback) controllers. We will develop a new multiplier method that allows for reduction of synthesis conditions to linear matrix inequality problems. We study conditions under which the reduction is exact (nonconservative) in the single-objective nominal setting. Although the multiplier method is conservative in the general setting of multi-objective robust control, numerical design examples demonstrate the utility of the method for the state feedback case.