Chaotic Control and Chaotification Using Fuzzy Approach

In this paper, we propose a fuzzy model-based methodology to deal with various control objectives for discrete-time chaotic systems from a unified viewpoint. With intent to unify the design process, we introduce a new design concept called virtual-desired-variable synthesis. Then, both the chaotic control and chaotification are eventually treated as a stabilization problem. Consequently, the conditions concerning the stability of the closed-loop system are formulated into LMIs. A feasible solution of the LMI problem guarantees the quadratical stability and gives the state feedback gains as well. The well-known Hénon map is used to demonstrate the unified approach.