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Mathematical Problems in Engineering
Volume 2013, Article ID 517258, 8 pages
Research Article

Stability Bound Analysis and Synthesis for Singularly Perturbed Systems with Time-Varying Delay

1Institute of Systems Science, Northeastern University, Shenyang 110819, China
2School of Information and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, China
3Mathematics Department, Jilin Normal University, Siping 136000, China

Received 22 September 2012; Revised 25 December 2012; Accepted 29 December 2012

Academic Editor: Baocang Ding

Copyright © 2013 Fengqi Sun 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 addresses the problems of stability bound analysis and synthesis for singularly perturbed systems with time-varying delay. First, by constructing an appropriate Lyapunov-Krasovskii functional, a sufficient condition is derived for the system to be stable when the singular perturbation parameter is lower than a predefined upper bound which is referred to as the stability bound of the singularly perturbed system. The proposed criterion needs less computational cost than the existing ones. Then, a state feedback controller design method is proposed to achieve a prescribed stability bound, which can be applied to both standard and nonstandard singularly perturbed systems with time-varying delay. Finally, the effectiveness and merits of the proposed approach are shown through numerical examples.