Abstract
It has been known that very complex chaotic behaviors can be observed in a simple first-order system with time-delay. This paper presents a fuzzy model-based approach for synchronization of time-delayed chaotic system via a scalar output variable. Takagi-Sugeno (T-S) fuzzy model can represent a general class of nonlinear system and we employ it for fuzzy modeling of the chaotic drive and response system with time-delay. Since only a scalar output variable is available for synchronization, a fuzzy observer based on T-S fuzzy model is designed and applied to chaotic synchronization. We analyze the stability of the overall fuzzy synchronization system by applying Lyapunov-Krasovskii theory and derive stability conditions by solving linear matrix inequalities (LMI's) problem. A numerical example is given to demonstrate the validity of the proposed synchronization approach.
| Original language | English |
|---|---|
| Pages (from-to) | 2593-2601 |
| Number of pages | 9 |
| Journal | International Journal of Bifurcation and Chaos in Applied Sciences and Engineering |
| Volume | 15 |
| Issue number | 8 |
| DOIs | |
| Publication status | Published - 2005 Jan 1 |
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All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Applied Mathematics
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Synchronization of time-delayed T-S fuzzy chaotic systems via scalar output variable. / Kim, Jae Hun; Shin, Hyunseok; Kim, Euntai; Park, Mignon.
In: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 15, No. 8, 01.01.2005, p. 2593-2601.Research output: Contribution to journal › Article
TY - JOUR
T1 - Synchronization of time-delayed T-S fuzzy chaotic systems via scalar output variable
AU - Kim, Jae Hun
AU - Shin, Hyunseok
AU - Kim, Euntai
AU - Park, Mignon
PY - 2005/1/1
Y1 - 2005/1/1
N2 - It has been known that very complex chaotic behaviors can be observed in a simple first-order system with time-delay. This paper presents a fuzzy model-based approach for synchronization of time-delayed chaotic system via a scalar output variable. Takagi-Sugeno (T-S) fuzzy model can represent a general class of nonlinear system and we employ it for fuzzy modeling of the chaotic drive and response system with time-delay. Since only a scalar output variable is available for synchronization, a fuzzy observer based on T-S fuzzy model is designed and applied to chaotic synchronization. We analyze the stability of the overall fuzzy synchronization system by applying Lyapunov-Krasovskii theory and derive stability conditions by solving linear matrix inequalities (LMI's) problem. A numerical example is given to demonstrate the validity of the proposed synchronization approach.
AB - It has been known that very complex chaotic behaviors can be observed in a simple first-order system with time-delay. This paper presents a fuzzy model-based approach for synchronization of time-delayed chaotic system via a scalar output variable. Takagi-Sugeno (T-S) fuzzy model can represent a general class of nonlinear system and we employ it for fuzzy modeling of the chaotic drive and response system with time-delay. Since only a scalar output variable is available for synchronization, a fuzzy observer based on T-S fuzzy model is designed and applied to chaotic synchronization. We analyze the stability of the overall fuzzy synchronization system by applying Lyapunov-Krasovskii theory and derive stability conditions by solving linear matrix inequalities (LMI's) problem. A numerical example is given to demonstrate the validity of the proposed synchronization approach.
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U2 - 10.1142/S0218127405013538
DO - 10.1142/S0218127405013538
M3 - Article
VL - 15
SP - 2593
EP - 2601
JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
SN - 0218-1274
IS - 8
ER -