Open AccessControlling fractional-order new chaotic system based on Lyapunov equation
Author(s) -
Zhe Xu,
Chongxin Liu,
Tiejun Yang
Publication year - 2010
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.59.1524
Subject(s) - chaotic , controller (irrigation) , control theory (sociology) , computer science , fractional order system , stability (learning theory) , order (exchange) , lyapunov stability , operator (biology) , lyapunov function , fractional calculus , lyapunov equation , chaotic systems , mathematics , lyapunov exponent , control (management) , physics , nonlinear system , finance , economics , gene , repressor , artificial intelligence , chemistry , biology , biochemistry , quantum mechanics , machine learning , transcription factor , agronomy
A new circuit unit for the analysis and synthesis of the chaotic behaviors in the new fractional-order system is proposed in this paper. Based on the approximation theory of fractional-order operator, an electronic circuit is designed to demonstrate the dynamic behaviors of the fractional-order Liu system with α=09 An effective controller is designed based on a theory of stability identification based on Lyapunov equation. The results between simulation and experiment are in good agreement, thereby proving the existence of chaos in the fractional-order new system and the effectiveness of our proposed control method.