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Journal of Control Science and Engineering
Volume 2011, Article ID 970962, 8 pages
Research Article

Robust Stability of a Class of Unstable Systems under Mixed Uncertainty

1Electrial Engineering Department, Engineering Faculty, Isra University, Amman, Jordan
2Computer Engineering Department, IUST University, Daraa, Syria

Received 9 April 2011; Accepted 16 September 2011

Academic Editor: L. Z. Yu

Copyright © 2011 Rami A. Maher and Raghad Samir. 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.


For unstable plants, the priority of control goes to the stability of synthesis, which means to find a stabilizer controller. In the case where the plant is subjected to structured and unstructured uncertainties, the stability problem becomes more crucial. The problem was solved by a conservative method based on generalized Kharitonov's theorem and Nevanlinna-Pick's interpolation (NPI) technique. This paper introduces a proposed straightforward numerical approach for loop shaping the unstructured additive or multiplicative maximum uncertainty magnitudes. The approach finds controllers, which are capable of stabilizing the interval system while the uncertainty box is enlarged to its maximum dimensions. To illustrate, we introduce some numerical examples.