A Fuzzy Lyapunov LMI Criterion to a Chaotic System

In terms of the Fuzzy Lyapunov method, this work proposes stability conditions for fuzzy logic control (FLC). Their application for chaotic systems can be approximated by the Tagagi-Sugeno (T-S) fuzzy model. The fuzzy Lyapunov function is defined as a fuzzy blending of quadratic Lyapunov functions. External forces or disturbances are not considered in the controlled systems. In the design controller procedure, a parallel distributed compensation (PDC) scheme is utilized to construct a global FLC by blending all linear local state feedback controllers. The stability criteria are found not only for fuzzy modeling but also for a real chaotic system. Furthermore, this controller design problem can be reduced to a linear matrix inequality (LMI) problem by use of the Schur Complements. Efficient interior-point algorithms are now available in Matlab toolbox to solve this type of problem.