Design of stable fuzzy control systems using Lyapunov's method in fuzzy hypercubes. (Q1408837)

A systematic procedure is presented to analyze and design a stable fuzzy controller for a class of nonlinear systems. Based on Lyapunov's direct method, the authors account for the relationship between the stability of the control system and the I/O sets of the fuzzy controller. First, the state space is partitioned into fuzzy hypercubes according to the product space of the input fuzzy sets of the states. Then, all fuzzy hypercubes are considered and made to satisfy Lyapunov's stability condition by choosing proper output centers of the associated fuzzy rules. Based on Lyapunov's stability method, a simple but more general methodology is proposed to analyse and design fuzzy controllers. The output of the fuzzy controller can be divided into two parts. One acts as linear state feedback to assign the poles of the control system to the desired positions. The other is used to guarantee the stability of the whole system. This approach can ease to handle the plant's uncertainties in different control regions. Through the proposed design guideline it is also possible to determine the performance and accuracy of fuzzy control systems. An example with a fuzzy controller for a chaotic system is presented to illustrate the design procedure.