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Mathematical Problems in Engineering
Volume 2012, Article ID 674087, 14 pages
Research Article

Indefinite LQ Control for Discrete-Time Stochastic Systems via Semidefinite Programming

College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao 266510, China

Received 19 October 2011; Accepted 29 November 2011

Academic Editor: Xue-Jun Xie

Copyright © 2012 Shaowei Zhou and Weihai Zhang. 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.


This paper is concerned with a discrete-time indefinite stochastic LQ problem in an infinite-time horizon. A generalized stochastic algebraic Riccati equation (GSARE) that involves the Moore-Penrose inverse of a matrix and a positive semidefinite constraint is introduced. We mainly use a semidefinite-programming- (SDP-) based approach to study corresponding problems. Several relations among SDP complementary duality, the GSARE, and the optimality of LQ problem are established.