Open AccessUniversal stabilisation design for a class of non‐linear systems with time‐varying input delays
Author(s) -
Cai Xiushan,
Lin Yuhang,
Liu Leipo
Publication year - 2015
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2014.1085
Subject(s) - backstepping , control theory (sociology) , class (philosophy) , mathematics , stability (learning theory) , computer science , mathematical optimization , control (management) , adaptive control , artificial intelligence , machine learning
The authors consider a universal stabilisation design for a class of non‐linear systems with time‐varying input delays in this study. Using the transport partial differential equation to express the delay, stability analysis is conducted with infinite‐dimensional backstepping transformations and by constructing a Lyapunov functional. Sufficient conditions are obtained, and a universal stabilisation formula is presented. Moreover, the stabilisation formula is optimal with respect to a meaningful cost functional. Finally, three examples are given to illustrate the effectiveness of the proposed design technique.