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New delay range–dependent stability criteria for interval time-varying delay systems via Wirtinger-based inequalities

Version 2 2024-06-04, 01:34
Version 1 2018-06-15, 15:21
journal contribution
posted on 2024-06-04, 01:34 authored by R Mohajerpoor, L Shanmugam, Hamid AbdiHamid Abdi, R Rakkiyappan, S Nahavandi, P Shi
Stability conditions for time-delay systems using the Lyapunov-based methodologies are generically expressed in terms of linear matrix inequalities. However, due to assuming restrictive conditions in deriving the linear matrix inequalities, the established stability conditions can be strictly conservative. This paper attempts to relax this problem for linear systems with interval time-varying delays. A double-integral inequality is derived inspired by Wirtinger-based single-integral inequality. Using the advanced integral inequalities, the reciprocally convex combination techniques and necessary slack variables, together with extracting a condition for the positive definiteness of the Lyapunov functional, novel stability criteria, have been established for the system. The effectiveness of the criteria is evaluated via 2 numerical examples. The results indicate that more complex stability criteria not only improve the stability region but also bring computational expenses.

History

Journal

International journal of robust and nonlinear control

Volume

28

Pagination

661-677

Location

Chichester, Eng.

ISSN

1049-8923

eISSN

1099-1239

Language

eng

Publication classification

C1 Refereed article in a scholarly journal

Copyright notice

2017, John Wiley & Sons, Ltd.

Issue

2

Publisher

Wiley