Synchronization of time-delayed T-S fuzzy chaotic systems via scalar output variable

Jae Hun Kim, Hyunseok Shin, Euntai Kim, Mignon Park

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 languageEnglish
Pages (from-to)2593-2601
Number of pages9
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume15
Issue number8
DOIs
Publication statusPublished - 2005 Jan 1

Fingerprint

Chaotic systems
Fuzzy Systems
Chaotic System
Synchronization
Scalar
Takagi-Sugeno Fuzzy Model
Output
Time Delay
Fuzzy Observer
Time delay
Chaotic Synchronization
Fuzzy Modeling
First-order System
Chaotic Behavior
Fuzzy Model
Stability Condition
Lyapunov
Matrix Inequality
Linear Inequalities
Linear matrix inequalities

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics

Cite this

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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.",
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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 journalArticle

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