Reachable Set Estimation and Controller Design for Linear Time-Delayed Control System with Disturbances

Yongchun Jiang; Hongli Yang; Ivan G. Ivanov

doi:10.20944/preprints202311.1327.v2

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preprints.org > computer science and mathematics > applied mathematics > doi: 10.20944/preprints202311.1327.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Reachable Set Estimation and Controller Design for Linear Time-Delayed Control System with Disturbances

Yongchun Jiang

Hongli Yang

^* ,

Ivan G. Ivanov

Version 1 : Received: 20 November 2023 / Approved: 21 November 2023 / Online: 21 November 2023 (13:45:55 CET)
Version 2 : Received: 29 December 2023 / Approved: 29 December 2023 / Online: 29 December 2023 (14:39:24 CET)

A peer-reviewed article of this Preprint also exists.

Jiang, Y.; Yang, H.; Ivanov, I.G. Reachable Set Estimation and Controller Design for Linear Time-Delayed Control System with Disturbances. Mathematics 2024, 12, 176. Jiang, Y.; Yang, H.; Ivanov, I.G. Reachable Set Estimation and Controller Design for Linear Time-Delayed Control System with Disturbances. Mathematics 2024, 12, 176.

Abstract

This paper investigates reachable set estimation and state-feedback controller design for linear time-delay control system with bounded disturbances. First, by constructing an appropriate Lyapunov-Krasovskii functional, we obtained a delay-dependent condition, which determed the admissible bounding ellipsoid for the reachable set of the system we considered. Then, a sufficient condition in form of liner matrix inequalities is given to solve the problem of controller design with reachable set estimation. Finally, by minimizing the volume of the ellipsoid and solving the liner matrix inequality, we obtain the desired ellipsoid and controller gain. A comparative numerical example is given to verify the usefulness of our result.

Keywords

time-delay; ellipsoid; Lyapunov-Krasovskii functional; reachable set; linear matrix inequalities

Subject

Computer Science and Mathematics, Applied Mathematics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Received: 29 December 2023
Commenter: Hongli YANG
Commenter's Conflict of Interests: Author

Comment: some revisions have been done.

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