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Mathematical Problems in Engineering
Volume 2017, Article ID 1414029, 9 pages
Research Article

Design of an Optimal Preview Controller for a Class of Linear Discrete-Time Descriptor Systems

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

Correspondence should be addressed to Fucheng Liao; nc.ude.btsu@oailcf

Received 23 January 2017; Accepted 8 May 2017; Published 12 June 2017

Academic Editor: Mohammad D. Aliyu

Copyright © 2017 Fucheng Liao et al. 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.


The preview control problem of a class of linear discrete-time descriptor systems is studied. Firstly, the descriptor system is decomposed into a normal system and an algebraic equation by the method of the constrained equivalent transformation. Secondly, by applying the first-order forward difference operator to the state equation, combined with the error equation, the error system is obtained. The tracking problem is transformed into the optimal preview control problem of the error system. Finally, the optimal controller of the error system is obtained by using the related results and the optimal preview controller of the original system is gained. In this paper, we propose a numerical simulation method for descriptor systems. The method does not depend on the restricted equivalent transformation.