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Mathematical Problems in Engineering
Volume 2015, Article ID 217904, 8 pages
Research Article

New Algorithm Based on Sign Decomposition to Verify the Robust Stability Property for a Class of Linear Time-Delay Systems

1ECEN, Texas A&M University, College Station, TX 77840, USA
2UAT-UAM Reynosa Rodhe, 88779 Reynosa, TAMPS, Mexico
3FIME, Universidad Autónoma de Nuevo León, 66450 San Nicolás de los Garza, NL, Mexico

Received 22 December 2014; Accepted 16 April 2015

Academic Editor: Baocang Ding

Copyright © 2015 Iván D. Díaz-Rodríguez 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.


The main focus of this paper is to analyze the robust stability property for a class of time-delay systems when parametric polynomic uncertainty is considered. The analysis is made by replacing the time-delay part with an auxiliary equation and then using the sign definite decomposition to deal with the polynomic parametric uncertainty. Also, it is shown that it is possible to verify the robust stability property by first obtaining the Hurwitz matrix from the characteristic equation for this class of systems and then checking the leading principal minors positivity using the sign definite decomposition. Finally, an algorithm codified in MATLAB is used to evaluate and graphically show the robust stability property. This is shown by a series of points that were calculated using the sign definite decomposition.