Chaotifying Continuous-Time TS Fuzzy Systems via Discretization

An approach is proposed for making a given stable continuous-time Takagi-Sugeno (TS) fuzzy-system chaotic, by first discretizing it and then using state feedback control of arbitrarily small magnitude. The feedback controller chosen among several candidates is a simple sinusoidal function of the system states, which can lead to uniformly bounded state vectors of the controlled system with positive Lyapunov exponents, and satisfy the chaotic mechanisms of stretching and folding, thereby yielding chaotic dynamics. This approach is mathematically proven for rigorous generation of chaos from a stable continuous-time TS fuzzy system, where the generated chaos is in the sense of Li and Yorke. A numerical example is included to visualize the theoretical analysis and the controller design. Manuscript received March 23, 2001; revised June 4, 2001. This work was supported by the Research Project Brain Korea 21. This paper was recommended by Associate Editor C. K. Tse. Z. Li and J. B. Park are with the Department of Electrical and Electronic Engineering, Yonsei University, Seoul 120-749, Korea (e-mail: [email protected]; [email protected]). Y. H. Joo is with the School of Electronic and Information Engineering, Kunsan National University, Kunsan, Chonbuk 573-701, Korea (e-mail: [email protected]). Publisher Item Identifier S 1057-7122(01)08988-7.