Componentwise state bounding of positive time-delay systems with disturbances bounded by a time-varying function

Abstract

This paper proposes a new method to solve the problem of finding the smallest componentwise upper bound of the state vector of a class of positive time-delay systems perturbed by unknown-but-bounded disturbances. Different from existing methods, which use only the constant maximum bound of the disturbance vector, our method exploits its known time-varying upper bound. As a result, a smaller upper bound, i.e. a more accurate state bound, is derived. A numerical example with some simulations is given to illustrate the effectiveness of our proposed method.

Keywords:

• Positive time-delay systems
• bounded disturbances
• componentwise state bound
• linear programming

Acknowledgments

The authors would like to thank the Editor, Dr. Andrea Lecchini-Visintini, and the anonymous reviewers for their useful comments which helped us improve both the quality and presentation of the paper.

Disclosure statement

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

Additional information

Funding

This research is funded by Vietnam National University Ho Chi Minh City (VNU-HCM) under grant number C2020-26-02.