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New delay range–dependent stability criteria for interval time‐varying delay systems via Wirtinger‐based inequalities
Author(s) -
Mohajerpoor Reza,
Shanmugam Lakshmanan,
Abdi Hamid,
Rakkiyappan Rajan,
Nahavandi Saeid,
Shi Peng
Publication year - 2017
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3893
Subject(s) - positive definiteness , mathematics , stability (learning theory) , interval (graph theory) , range (aeronautics) , linear matrix inequality , control theory (sociology) , inequality , matrix (chemical analysis) , lyapunov function , regular polygon , stability criterion , multiple integral , mathematical optimization , positive definite matrix , computer science , mathematical analysis , nonlinear system , eigenvalues and eigenvectors , control (management) , statistics , engineering , artificial intelligence , aerospace engineering , composite material , geometry , quantum mechanics , machine learning , physics , combinatorics , materials science , discrete time and continuous time
Summary 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.