Fuzzy Chaos Synchronization via Sampled Driving Signals

In this chapter the Tagaki-Sugeno fuzzy model representation of a chaotic system is used to find an alternative solution to the chaos synchronization problem. One of the advantages of the proposed approach is that it allows to express the synchronization problem as a fuzzy logic observer design in terms of linear matrix inequalities, which can be solved numerically using readily advailable software packages. Also, given the linear nature of this fuzzy representation, it is possible to use sophisticated methodologies to consider the more practical problem of digital implementation of a synchronization design. In particular, in this contribution the problem of a

master-slave

chaos synchronization design from sampled drive signals is considered and a solution is proposed as the state-matching digital redesign of the fuzzy logic observer designed to solve the continuous-time synchronization problem. The effectiveness of the proposed synchronization method is illustrated through numerical simulations of three well-known benchmark chaotic system, namely, Chua’s circuit, Chen’s equation, and the Duffing oscillator.