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Journal of Applied Mathematics
Volume 2012, Article ID 638762, 14 pages
Research Article

Discrete-Time Indefinite Stochastic LQ Control via SDP and LMI Methods

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

Received 10 August 2011; Accepted 4 December 2011

Academic Editor: Oluwole D. Makinde

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 studies a discrete-time stochastic LQ problem over an infinite time horizon with state-and control-dependent noises, whereas the weighting matrices in the cost function are allowed to be indefinite. We mainly use semidefinite programming (SDP) and its duality to treat corresponding problems. Several relations among stability, SDP complementary duality, the existence of the solution to stochastic algebraic Riccati equation (SARE), and the optimality of LQ problem are established. We can test mean square stabilizability and solve SARE via SDP by LMIs method.