A new approach to state bounding for coupled differential-difference equations with bounded disturbances

Abstract

In this paper, we present a new method to the state bounding problem for a class of coupled differential-difference equations (CDDEs) with bounded disturbances and time-varying delays. Instead of using the state transformation to reformulate the considered problem into the one for non-perturbed CDDEs, our novel idea is to construct suitable comparison systems, from which the state vector can be estimated directly and the information on the initial value is exploited more effectively in order to derive a sharper state bound. For computing and minimising the state bound, a numerical linear programming-based algorithm is also presented. The effectiveness of the presented method is verified via two numerical examples.

Keywords:

• State bounding
• coupled differential-difference equations (CDDEs)
• time-varying delay
• bounded disturbances
• solution comparison
• linear programming

Acknowledgments

The author would like to thank the referees for their useful comments and valuable suggestions which helped to improve the manuscript.

Disclosure statement

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

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.

Additional information

Funding

This research was supported by the Ministry of Education and Training (Bô Giáo dçc và Dào tço) [grant number B2023-DQN-03], Vietnam.