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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 853415, 9 pages
Research Article

Singular LQ Problem for Irregular Singular Systems

1School of Science, China Jiliang University, Hangzhou 310018, China
2School of Mathematics, Shandong University, Jinan 310018, China

Received 26 April 2014; Accepted 25 June 2014; Published 8 July 2014

Academic Editor: Jong Hae Kim

Copyright © 2014 Qingxiang Fang 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.


This paper is concerned with the singular LQ problem for irregular singular systems with persistent disturbances. The full information feedback control method is employed to achieve the optimal control. By restricted system equivalence transformation, the system state is decomposed into free state and restricted state and the input is decomposed into free input and forced input. Some sufficient conditions for the unique existence of optimal control-state pair are derived and these conditions are all described unitedly with matrix rank equalities. The optimal control-state pair can be explicitly formulated via solving an algebraic Riccati equation and a Sylvester equation. Moreover, under the optimal control-state pair, the resulting system has no free state.