This paper discusses optimal H∞ control synthesis via discrete Riccati equations for discrete linear periodically time-varying (LPTV) systems. Based on the results presented in [1], an explicit minimum entropy H∞ controller for general time-varying systems is obtained. The control synthesis technique is subsequently applied to LPTV systems and it is shown that the resulting controllers are also periodically time varying. In order to demonstrate the effectiveness of the proposed control synthesis technique, both single-rate and multi-rate discrete-time minimum entropy H∞ track-following control designs for hard disk drives are considered. It is shown, via a comprehensive simulation study, that track-following controllers designed using the H∞ synthesis technique proposed in this paper achieve the robust performance of a desired error rejection function. Moreover, as expected, multi-rate controllers has the ability of outperforming their single-rate counterparts.
