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The estimation of a robust domain of attraction using Gershgorin theorem
Author(s) -
KazakovaFrehse N.,
Frick K.
Publication year - 1998
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(199803)8:3<295::aid-rnc317>3.0.co;2-o
Subject(s) - eigenvalues and eigenvectors , mathematics , lyapunov function , domain (mathematical analysis) , algebraic number , nonlinear system , quadratic equation , matrix (chemical analysis) , control theory (sociology) , mathematical analysis , computer science , physics , geometry , control (management) , artificial intelligence , materials science , quantum mechanics , composite material
In this paper a method of determining a radius of a guaranteed robust region of attraction for nonlinear closed‐loop uncertain systems is presented. The radius formula contains parameter‐dependent eigenvalues of the matrix of the parametrized quadratic Lyapunov function. As these eigenvalues usually are not analytically calculable, one can apply an algebraic estimation technique for eigenvalues. In this paper the concept of Gershgorin discs is used. A numerical example is included for a second‐order system. © 1998 John Wiley & Sons, Ltd.