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A generalized discretization scheme of Lyapunov functional in the stability problem of linear uncertain time‐delay systems
Author(s) -
Gu Keqin
Publication year - 1999
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/(sici)1099-1239(199901)9:1<1::aid-rnc382>3.0.co;2-s
Subject(s) - discretization , mathematics , stability (learning theory) , lyapunov function , limit (mathematics) , piecewise linear function , linear matrix inequality , piecewise , mathematical optimization , quadratic equation , linear system , scheme (mathematics) , control theory (sociology) , computer science , nonlinear system , control (management) , physics , geometry , quantum mechanics , machine learning , artificial intelligence , mathematical analysis
The stability problem of linear uncertain time‐delay systems is considered using a quadratic Lyapunov functional. The kernel of the functional, which is a function of two variables, is chosen as piecewise linear. As a result, the stability condition can be written as a linear matrix inequality, which improves the estimate of stability limit over the existing approaches. A number of constraints on the parameters can be introduced to reduce the computational effort needed with some compromised accuracy. For a particular choice of constraints, the existing discretization scheme can be recovered. Copyright © 1999 John Wiley & Sons, Ltd.