Abstract
In this paper, we propose a new adaptive \(\mathcal H_\infty\) synchronization strategy, called an adaptive fuzzy delayed feedback \(\mathcal H_\infty\) 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 \(\mathcal H_\infty\) control scheme, the AFDFHS controller is presented such that the synchronization error system is asymptotically stable with a guaranteed \(\mathcal{H}_{\infty }\) 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.
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AHN, C.K. Robust chaos synchronization based on adaptive fuzzy delayed feedback \({\bf{\mathcal{H}}}_{\bf{\infty}}\) control. Pramana - J Phys 78, 361–374 (2012). https://doi.org/10.1007/s12043-011-0239-4
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DOI: https://doi.org/10.1007/s12043-011-0239-4
Keywords
- Chaos synchronization
- Takagi–Sugeno (T–S) fuzzy model
- adaptive \(\mathcal H_\infty\)control
- linear matrix inequality (LMI)
- delayed feedback control