Design of a time-delay feedback controller to chaotify continuous-time Takagi-Sugeno fuzzy systems

An approach based on time-delay feedback control is proposed to make a given stable continuous-time Takagi-Sugeno (TS) fuzzy system chaotic. It comprises fuzzy feedback linearisation and a suitable approximate relationship between a time-delay differential equation and a discrete map. The time-delay feedback controller is a simple sinusoidal function of the system's delay states, which has arbitrarily small amplitude. This approach is mathematically proven correct for rigorous generation of chaos from continuous-time TS fuzzy systems, where the generated chaos fulfills the definition of Li and Yorke. Numerical examples are included to visualize the theoretical analysis and the controller design.