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Mathematical Problems in Engineering
Volume 2016, Article ID 2879724, 10 pages
Research Article

Design of Optimal Output Regulators for Dual-Rate Linear Discrete-Time Systems Based on the Lifting Technique

School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China

Received 22 January 2016; Accepted 2 June 2016

Academic Editor: Qingling Zhang

Copyright © 2016 Yujian Guo and Fucheng Liao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A design strategy of optimal output regulators for dual-rate discrete-time systems, whose output sampling period is an integer multiple of the input updating period, is proposed. At first, by using the discrete lifting technique, the dual-rate discrete-time system is converted to a single-rate augmented system in form and the lifted state-space model is constructed. Correspondingly, the performance index of the original system is modified to the performance index of the single-rate augmented system. And the original problem is transformed into an output regulation problem for the augmented system. Then, according to the optimal regulator theory, an optimal output regulator for the dual-rate discrete-time system is derived. In the meantime, the existence conditions of the optimal output regulator are discussed. Finally, a numerical example is included to illustrate the effectiveness of the proposed method.