Open AccessApproach to delay‐dependent robust stability and stabilisation of delta operator systems with time‐varying delays
Author(s) -
El Aiss Hicham,
Rachid Hafsaa,
Hmamed Abdelaziz,
El Hajjaji Ahmed
Publication year - 2018
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.2017.0006
Subject(s) - delta operator , control theory (sociology) , small gain theorem , stability (learning theory) , transformation (genetics) , model transformation , mathematics , operator (biology) , term (time) , linear matrix inequality , computer science , mathematical optimization , shift operator , control (management) , consistency (knowledge bases) , repressor , artificial intelligence , compact operator , chemistry , biochemistry , geometry , quantum mechanics , machine learning , transcription factor , programming language , physics , extension (predicate logic) , gene
This study investigates the problem of delay‐dependent stability and stabilisation of uncertain delta operator systems with time‐varying delay. A new model transformation is proposed using a three‐term approximation, which has a smaller approximation error than the existing methods based on one or two terms. On the basis of scaled small gain theorem (scaled small gain) and an appropriate Lyapunov–Krasovskii functional, a new stability criterion is proposed in terms of linear matrix inequalities. Finally, numerical examples are presented to illustrate the effectiveness of the proposed method.