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Linear functional state bounding for perturbed time-delay systems and its application

Version 2 2024-06-03, 12:03
Version 1 2015-02-24, 12:20
journal contribution
posted on 2024-06-03, 12:03 authored by PT Nam, Pubudu PathiranaPubudu Pathirana, Hieu TrinhHieu Trinh
This paper considers time-delay systems with bounded disturbances. We study a new problem of finding an upper bound of an absolute value function of any given linear functional of the state vector starting from the origin of the system. Based on the Lyapunov-Krasovskii method combining with the recent Wirtinger-based integral inequality that has just been proposed by Seuret & Gouaisbaut (2013. Wirtinger-based integral inequality: application to time-delay systems. Automatica, 49, 2860-2866), sufficient conditions for the existence of an upper bound of the function are derived. The obtained results are shown to be more effective than those adapted from the existing works on reachable set bounding. Furthermore, the obtained results are applied to refine existing ellipsoidal bounds of the reachable sets. The effectiveness of the obtained results is illustrated by two numerical examples.

History

Journal

IMA Journal of mathematical control and information

Volume

32

Pagination

245-255

Location

Oxford, Eng.

ISSN

0265-0754

eISSN

1471-6887

Language

eng

Publication classification

C Journal article, C1 Refereed article in a scholarly journal

Copyright notice

2015, Oxford University Press

Publisher

Oxford University Press