New delay-dependent absolute stability criteria for Lur'e systems with time-varying delay

Abstract

In this article, the absolute stability problem is investigated for Lur'e systems with time-varying delay and sector-bounded nonlinearity. By employing the delay fractioning idea, the new augmented Lyapunov functional is first constructed. Then, by introducing some slack matrices and by reserving the useful term when estimating the upper bound of the derivative of Lyapunov functional, the new delay-dependent absolute stability criteria are derived in terms of linear matrix inequalities. Several numerical examples are presented to show the effectiveness and the less conservativeness of the proposed method.

Keywords:

• absolute stability
• Lur'e systems
• time-varying delay
• linear matrix inequalities

Acknowledgements

The authors would like to thank the anonymous reviewers for their constructive comments and suggestions to improve the quality of the article. This work was supported by the National Natural Science Foundation of P.R. China under Grant 60850004.