Stability Analysis of Nonlinear Dynamic Systems by Nonlinear Takagi–Sugeno–Kang Fuzzy Systems

This paper proposes a systematic procedure to address the limit cycle prediction of a Nonlinear Takagi–Sugeno–Kang (NTSK) fuzzy control system with adjustable parameters. NTSK fuzzy can be linearized by describing function method. The stability of the equivalent linearized system is then analyzed using the stability equations and the parameter plane method. After that the gain–phase margin (PM) tester has been added, then gain margin (GM) and phase margin for limit cycle are analyzed. Using NTSK fuzzy control system can help to have fewer rules. In order to analyze the stability with the same technique of stability analysis, the results of NTSK fuzzy control system will be compared with Dynamic fuzzy control system [1]. Computer simulations show differences between both systems.