Robust fuzzy stabilization of dithered chaotic systems using island-based random optimization algorithm

Zhi Ren Tsai, Yau Zen Chang, Jiing Dong Hwang*, Jye Lee

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

15 Scopus citations


Applying dither to highly nonlinear systems may suppress chaotic phenomena, but dynamic performance, such as convergence rate and disturbance attenuation, is usually not guaranteed. This paper presents a dithered H robust fuzzy control scheme to stabilize chaotic systems that ensures disturbance attenuation bounds. In the proposed scheme, Takagi-Sugeno (T-S) fuzzy linear models are used to describe the relaxed models of the dithered chaotic system, and fuzzy controllers are designed based on an extension to the concept of parallel distributed compensation (PDC). Sufficient condition for the existence of the H robust fuzzy controllers is presented in terms of a novel linear matrix inequalities (LMI) form which takes full consideration of modeling error and disturbances, but cannot be solved by the standard procedures. In order to solve the LMI problem and to identify the chaotic systems as T-S fuzzy modes, we propose a compound optimization strategy called the island-based random-walk algorithm (IRA). The algorithm is composed of a set of communicating random-walk optimization procedures concatenated with the down-hill simplex method. The design procedure and validity of the proposed scheme is demonstrated via numerical simulation of the dithered fuzzy control of a chaotic system.

Original languageEnglish
Pages (from-to)1171-1188
Number of pages18
JournalInformation Sciences
Issue number4
StatePublished - 15 02 2008


  • Chaotic systems
  • Dither
  • H robust fuzzy control
  • Linear matrix inequality


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