Fuzzy-chaos H∞ control for nonlinear systems

A new fuzzy model-based fuzzy-chaos H_∞ controller is proposed for chaotic systems and a kind of nonlinear systems which can produce chaotic attractor. Due to the ergodity of chaos, controlled systems move to the convex domain including desired state. Once the system states come into the convex domain, the open-loop control is cut off and Takagi-Sugeno fuzzy model-based H_∞ controller is employed. With fuzzy-chaos H_∞ controller, the controlled systems is stabilized on desired state. Linear matrix inequality approach is used to design close-loop controller, and the sufficient conditions of H_∞ controller existence are achieved, which can guarantee the quadratic stability of the controlled plant. Finally, simulation of Lorenz chaos is carried out. The results show that the designed fuzzy-chaos H_∞ controller stabilize effectively nonlinear systems whose H_∞ norm is less than γ.