Asymptotic Stabilization of a Morphous One- Parameter Chaotic System

 Abstract—The asymptotic stabilization of a morphous oneparameter chaotic system using Takagi Sugeno Fuzzy Controllers is reported in this paper. This system is a parametrically modified system realized from the generalized canonical Lorenz system and having only one variable parameter. The system has been proved to be topologically nonequivalent to the classic Lorenz system but generate attractors that morph from Lorenz-like to Chen-like as the parameter is varied positively. A Fuzzy Controller designed via Takagi Sugeno Fuzzy models and stability analysis of the Lyapunov stability type is used to stabilize the system's trajectories in the sense of Lyapunov. Numerical simulation and analysis of fuzzy rules shows that the system converges to equilibrium points with better settling times as the parameter is varied positively. Moreover, the control effort of each fuzzy subsystems formed by the fuzzy rules are over 1/10 less in comparison with stabilization of the classic Lorenz system via the same design principles.