ε-bounded state estimation for time-delay systems with bounded disturbances

Abstract

A new problem on ε-bounded functional state estimation for time-delay systems with unknown bounded disturbances is studied in this paper. In the presence of unknown bounded disturbances, the common assumption regarding the observer’s matching condition is no longer required. In this regard, instead of achieving asymptotic convergence for the observer error, the error is now required to converge exponentially within a ball with a small radius ε > 0. This means that the estimate converges exponentially within an ε-bound of the true value. A general observer that utilises multiple-delayed output and input information is proposed. Sufficient conditions for the existence of the proposed observer are first given. We then employ an extended Lyapunov–Krasovskii functional which combines the delay-decomposition technique with a triple-integral term to study the ε-convergence problem of the observer error system. Moreover, the obtained results are shown to be more effective than the existing results for the cases with no disturbances and/or no time delay. Three numerical examples are given to illustrate the obtained results.

Keywords:

• ε-bounded state estimation
• time-delay systems
• unknown bounded disturbances

Acknowledgements

The authors would like to thank the reviewers and the editor-in- chief for their very helpful comments and suggestions, which have improved our paper.

Additional information

Funding

This work is supported by the Vietnam Institute for Advanced Study in Mathematics and the Australian Research Council under the discovery grant [grant number DP130101532].