Open AccessA stability theorem about fractional systems and synchronizing fractional unified chaotic systems based on the theorem
Author(s) -
Jinbo Hu,
Huiyu Yan,
Lanhao Zhao
Publication year - 2009
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.58.4402
Subject(s) - synchronizing , stability theorem , lyapunov stability , stability (learning theory) , mathematics , picard–lindelöf theorem , fractional calculus , converse , chaotic systems , lyapunov function , order (exchange) , lyapunov exponent , small gain theorem , chaotic , brouwer fixed point theorem , fixed point theorem , pure mathematics , mathematical analysis , computer science , topology (electrical circuits) , physics , nonlinear system , combinatorics , artificial intelligence , cauchy distribution , geometry , quantum mechanics , machine learning , finance , economics , control (management)
A stability theorem is proposed and proved for fractional system whose order is not greater than 1 according with Lyapunov stability theorem and Lyapunov converse theorem. Using this theoremfractional unified chaotic systems with unknown parameter are synchronized adaptively. Numerical simulation certifies effectiveness of the theorem.