Open AccessImproved approach to delay‐dependent stability and stabilisation of two‐dimensional discrete‐time systems with interval time‐varying delays
Author(s) -
Peng Dan,
Hua Changchun
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.2014.0886
Subject(s) - control theory (sociology) , mathematics , interval (graph theory) , weighting , stability (learning theory) , discrete time and continuous time , stability criterion , matrix (chemical analysis) , basis (linear algebra) , state (computer science) , control (management) , computer science , algorithm , medicine , statistics , materials science , combinatorics , artificial intelligence , machine learning , composite material , radiology , geometry
Two recent Lyapunov‐based methods: free weighting matrix approach and Jensen inequality approach, have reduced the conservatism and the complexity of the stability result for one‐dimensional (1D) time‐delay systems, respectively. In this study, the authors further concern the analysis of delay‐dependent stability and stabilisation for two‐dimensional (2D) discrete systems with interval time‐varying delays. By applying a new Lyapunov functional combining with the approaches of 2D Jensen inequalities and free weighting matrices, a new delay‐dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). Compared with the existing result, less decision variables are involved in the stability condition, so the burden of numerical computation is reduced greatly. It is also rigorously proved that the author's result is less conservative than some recent ones. On the basis of the stability criterion, state feedback is considered to realise the stability control and the state feedback gain can be solved by LMIs. Numerical examples show the effectiveness and advantage of their results.