Design of sliding-mode observer with uncertain time delay based on LMI

Abstract

The design of observers for a linear system with unknown, time-varying time delay is still an open problem in the field of structural control. A class of sliding-mode observer with state and input time-varying delay is developed from the basis of the coordinate transformation and free-weighting matrix methods. The delay-dependent and delay-rate-dependent conditions formulated by linear matrix inequalities are proposed to find the gains of the observers. The dynamic properties of the observers are also discussed. Finally, a numerical example of a fourth-order system is used to show the feasibility of the main results.

Keywords:

• sliding-mode observer
• time delay
• input delay
• LMI

Acknowledgements

The authors would like to thank the reviewers for their very helpful comments and suggestions that have improved the presentation of this paper. The work of Faxiang XIE was supported by the Natural Science Foundation of Jiangsu province under Grant BK2012412.