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Delay‐dependent conditions for finite time stability of linear time‐varying systems with delay
Author(s) -
Chen Menghua,
Sun Jian
Publication year - 2020
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.2059
Subject(s) - mathematics , control theory (sociology) , stability (learning theory) , interval (graph theory) , discretization , time complexity , matrix (chemical analysis) , linear matrix inequality , linear system , differential (mechanical device) , mathematical optimization , computer science , algorithm , mathematical analysis , control (management) , engineering , materials science , combinatorics , machine learning , artificial intelligence , composite material , aerospace engineering
This paper investigates the problem of finite time stability of linear time‐varying system with delay. By constructing an augmented time‐varying Lyapunov functional and using the Wirtinger‐type inequality deductively, delay‐dependent finite time stability conditions are derived and presented in terms of differential linear matrix inequalities (DLMIs). Then, the DLMIs are transformed into a series of recursive linear matrix inequalities (RLMIs) by discretizing the time interval into equally spaced time distances, and an algorithm is given to solve the RLMIs. Examples illustrate the feasibility and effectiveness of the proposed method.