An approach to anticontrol of chaos for a discrete-time TS fuzzy system

An approach is proposed for making a given stable Takagi-Sugeno (TS) fuzzy system chaotic by 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 the rigorous generation of chaos from a stable TS fuzzy system, where the chaos is in the sense of Li and Yorke. A numerical example is included to visualize the theoretical analysis and the controller design.