New stability criteria of linear singular systems with time-varying delay

Abstract

Most of the existing results on the stability problem of delayed singular systems only pertain to the case of constant delay. This is due to the fact that time-varying delay makes it hardly possible to explicitly express the fast variables. In this paper, aiming at dealing with the case of time-varying delay, we create a way to prove the stability by using a perturbation approach. Rather, we first get the decay rate for slow variables by using Lyapunov functional approach and, furthermore, guarantee that the fast variables fall into decay by characterising their effect on the derived decay rate. Also, we present a convexity technique in computing the constructed Lyapunov functional which contributes to the elimination of the possible conservatism caused by the varying rate of delay. Finally, we provide two numerical examples to demonstrate the effectiveness of the method.

Keywords:

• singular systems
• time-delay
• exponential stability
• Lyapunov exponent

Acknowledgements

The author would like to thank the anonymous reviewers for their helpful and insightful comments for improving the quality of this paper. This work is supported by the National Natural Science Foundation of China under Grants 61104119 and 61273120. The author is supported by Reserve Talents of Universities Overseas Research Program of Heilongjiang.

Additional information

Notes on contributors

Shen Cong

Shen Cong was born in 1976. He received the BS degree and the MS degree in power system and its automation, respectively, from the Wuhan University of Hydraulic and Electrical Engineering, Wuhan, China, in 1999 and Hohai University, Nanjing, China, in 2002, and the PhD degree in control theory and control engineering from the Southeast University, Nanjing, China, in 2007. From 2007–2009, he was a lecturer at the Nanjing University of Science and Technology. Now, he is an associate professor at Heilongjiang University. His research interests include stochastic systems, time-delay systems and non-linear control systems.