Chaotifying TS Fuzzy Systems

Abstract

In this chapter, chaotifying both discrete-time and continuous-time Takagi-Sugeno (TS) fuzzy systems is introduced. To chaotify discrete-time TS fuzzy systems, the parallel distributed compensation (PDC) method is employed to determine the structure of a fuzzy controller so as to make all Lyapunov exponents of the controlled TS fuzzy system strictly positive. But for continuous-time ones, the chaotification approach is based on fuzzy feedback linearization and a suitable approximate relationship between a time-delay differential equation and a discrete map. The time-delay feedback controller, chosen among several candidates, is a simple sinusoidal function of the delay states of the system, which can have an arbitrarily small amplitude. These anti-control approaches are all proved to be mathematically rigorous in the sense of Li and Yorke. Some examples are given to illustrate the effectiveness of the proposed anti-control methods.