Journal of Applied Mathematics
Volume 2012 (2012), Article ID 532912, 12 pages
Research Article

On Exponential Stability Conditions of Descriptor Systems with Time-Varying Delay

School of Mechanical & Electrical Engineering, Heilongjiang University, Harbin 150080, China

Received 8 August 2011; Revised 4 November 2011; Accepted 4 November 2011

Academic Editor: Kai Diethelm

Copyright © 2012 S. Cong and Z.-B. Sheng. 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.


We are interested in the exponential stability of the descriptor system, which is composed of the slow and fast subsystems with time-varying delay. In computing a kind of Lyapunov functional, we employ a necessary number of slack matrices to render the balance and to yield the convexity condition for reducing the conservatism and dealing with the case of time-varying delay. Therefore, we can get the decay rate of the slow variables. Moreover, we characterize the effect of the fast subsystem on the derived decay rate and then prove the fast variables to decay exponentially through a perturbation approach. Finally, we provide an example to demonstrate the effectiveness of the method.