Open AccessFinite‐time stability and stabilisation of distributed parameter systems
Author(s) -
Li Xueyang,
Mao Weijie
Publication year - 2017
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.2016.1087
Subject(s) - control theory (sociology) , stability (learning theory) , distributed parameter system , state (computer science) , stability conditions , computer science , mathematics , control (management) , algorithm , discrete time and continuous time , mathematical analysis , machine learning , artificial intelligence , statistics , differential equation
This study addresses the problems of finite‐time (FT) stability and stabilisation for distributed parameter systems. First, the authors extend the concepts of FT stability and FT stabilisation to the distributed parameter systems. Then, sufficient conditions of the L 2 ‐FT stability and W 1,2 ‐FT stability for the distributed parameter systems are established in terms of linear matrix inequalities. Based on these sufficient conditions, the authors design the state feedback controllers which guarantee the closed‐loop distributed parameter systems to be L 2 ‐FT stable and W 1,2 ‐FT stable, respectively. Finally, numerical examples are given to illustrate the proposed results.