Output Feedback Control of Multirate Sampled-Data Systems with Frequency Specifications

This paper addresses the problem of H_∞ output feedback controller design of multirate sampled-data systems with frequency specifications. The general multirate situation is considered, where not only the inputs and outputs but also different channels of the inputs or the outputs have different sampling rates. The aim of this paper is to design an output feedback controller for multirate sampled-data systems in order to ensure an H_∞ performance level over a restricted frequency, which includes the standard H_∞ control problem as a special case and can better reflect the requirement of attenuating disturbances over restricted frequency ranges. The problem is solved via reformulating the multirate sampled-data system with an output feedback controller and utilizing the generalized Kalman-Yakubovič-Popov lemma to deal with the restricted frequency specifications. For a given restricted frequency range, convex conditions are derived for the existence of a required controller and cases for low/high/entire frequency ranges are also addressed specifically. Finally, illustrative examples are presented to show the effectiveness and advantage of the proposed controller design methods.