New results on delay-dependent robust stability of uncertain time delay systems

Abstract

This article considers delay-dependent robust stability for linear uncertain systems with time delay. The delay is assumed to be constant and unknown, but its upper bound is known. The uncertainty is assumed to be time-varying structured uncertainties. By introducing augmented Lyapunov functional and using free-weighting matrix method, the improved delay-dependent stability and robust stability conditions will be obtained by means of linear matrix inequalities. Theoretical and numerical examples comparison suggest that the proposed conditions are less conservative than existing ones.

Keywords:

• linear systems
• time delay
• robust stability
• LMIs

Acknowledgements

The authors are grateful to associate editor and the anonymous referees and Prof. Chong Lin for their careful reading and constructive comments and suggestions which helped improving the presentation of this article. This work is partially supported by the Natural Science Foundation of China (60674055, 60774047) and the Taishan Scholar Programme of Shandong Province.