Analysis and control for a T-S fuzzy chaotic system

A three-dimensional quadratic smooth continuous autonomous chaotic system with nine parameters is derived in this paper. The system exists three quadratic terms including two quadratic cross-product terms and one quadratic square term. Basic dynamical behaviors including Lyapunov exponents and dissipation are analyzed respectively. A nonlinear controller and a linear controller are designed to guarantee the closed-loop system be stable respectively via a state feedback approach. Compared with the nonlinear T-S fuzzy controller, the linear controller is simpler in structure and can stabilize rapidly the chaotic system within finite time by verifying numerical simulations.