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https://www.ias.ac.in/article/fulltext/pram/078/03/0361-0374

Chaos synchronization; Takagi–Sugeno (T–S) fuzzy model; adaptive $\mathcal_{\infty}$ control; linear matrix inequality (LMI); delayed feedback control.

In this paper, we propose a new adaptive $\mathcal_{\infty}$ synchronization strategy, called an adaptive fuzzy delayed feedback $\mathcal_{\infty}$ synchronization (AFDFHS) strategy, for chaotic systems with uncertain parameters and external disturbances. Based on Lyapunov–Krasovskii theory, Takagi–Sugeno (T–S) fuzzy model and adaptive delayed feedback $\mathcal_{\infty}$ control scheme, the AFDFHS controller is presented such that the synchronization error system is asymptotically stable with a guaranteed $\mathcal_{\infty}$ performance. It is shown that the design of the AFDFHS controller with adaptive law can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed AFDFHS approach.

Choon Ki Ahn¹

1. Faculty of the Department of Automotive Engineering, Seoul National University of Science & Technology, 172 Gongneung 2-dong, Nowon-gu, Seoul 139-743, Korea

Published

March 2012

Manuscript received

5 October 2010

Manuscript revised

1 September 2011

Accepted

14 October 2011