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Mathematical Problems in Engineering
Volume 2016, Article ID 6142848, 12 pages
Research Article

Specific -Admissibility and Design Issues for Uncertain Descriptor Systems with Parametric Uncertainty in the Derivative Matrix

Department of Computer Science, University of Taipei, Taipei 100, Taiwan

Received 30 October 2015; Revised 8 January 2016; Accepted 10 January 2016

Academic Editor: Yan-Jun Liu

Copyright © 2016 Chih-Peng Huang. 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.


Stability analysis issues and controller synthesis for descriptor systems with parametric uncertainty in the derivative matrix are discussed in this paper. The proposed descriptor system can extend the system’s modeling extent of physical and engineering systems from the traditional state-space model. First, based on the extended -stability definitions for the descriptor model, necessary and sufficient admissibility and -admissibility conditions for the unforced nominal descriptor system are derived and formulated by compact forms with strict linear matrix inequality (LMI) manner. In contrast, existing results need to involve nonstrict LMIs, which cannot be evaluated by current LMI solvers and need some extra treatments. Deducing from the obtained distinct results, the roust admissibility and -admissibility of the descriptor system with uncertainties in both the derivative matrix and the system’s matrices thus can be coped. Furthermore, by involving a proportional and derivative state feedback (PDSF) control law, we further address the controller design for the resulting closed-loop systems. Since all the proposed criteria are explicitly expressed in terms of the strict LMIs, we can use applicable LMI solvers for evaluating the feasible solutions. Finally, the efficiency and practicability of the proposed approach are demonstrated by two illustrative examples.