A numerical method for filtering of linear systems with distributed delays

Abstract

This paper presents a numerical approach to solve the estimator-based filtering problem of a linear system with multiple and distributed delays. We consider the problem of finding a filter or estimator that suppresses the ${\mathcal{H}}_2$ filtering cost on the transfer matrix from a given noise input to the filtering error. By solving an optimisation problem associated with the ${\mathcal{H}}_2$ performance, the gain matrices of the filter are obtained. The effectiveness of the presented approach is illustrated by numerical simulations.

Keywords:

• Linear delay systems
• ${\mathcal{H}}_2$ filtering
• optimisation

Acknowledgments

The authors are greatly indebted to Dr. Alexandre Seuret and the anonymous reviewers for their valuable comments and suggestions, which have greatly improved the quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 62073098, U1913209] and Shenzhen Fundamental Research Program [grant numbers JCYJ20200109113210134, JCYJ20210324132215038].