Stabilization of a 4D Quadratic Polynomial Chaotic System with No Constant Term via a T-S Fuzzy Control Approach

A problem on stabilization of a 4D quadratic polynomial chaotic system with five linear terms and six nonlinear terms is investigated in this paper. The chaotic system with complex structures has no any constant term. The origin is one of the equilibria. Dynamical behaviors including offset boosting are analyzed. The 4D polynomial chaotic system can be converted into a T-S fuzzy model with two simple rules. A local T-S fuzzy model is constructed successfully. Based on a linear matrix inequality approach, a local T-S fuzzy controller is designed effectively to stabilize the 4D polynomial chaotic system within a finite time.