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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 683797, 14 pages
http://dx.doi.org/10.1155/2014/683797
Research Article

On the Solution of a Nonlinear Semidefinite Program Arising in Discrete-Time Feedback Control Design

Department of Mathematics, Faculty of Science, Alexandria University, Moharam Bey, Alexandria 21511, Egypt

Received 20 May 2013; Accepted 11 November 2013; Published 2 January 2014

Academic Editor: Jung-Fa Tsai

Copyright © 2014 El-Sayed M. E. Mostafa. 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.

Abstract

A sequential quadratic programming method with line search is analyzed and studied for finding the local solution of a nonlinear semidefinite programming problem resulting from the discrete-time output feedback problem. The method requires an initial feasible point with respect to two positive definite constraints. By parameterizing the optimization problem we ease that requirement. The method is tested numerically on several test problems chosen from the benchmark collection (Leibfritz, 2004).