Fuzzy model based control: stability, robustness, and performance issues

A nonlinear controller based on a fuzzy model of MIMO dynamical systems is described and analyzed. The fuzzy model is based on a set of ARX models that are combined using a fuzzy inference mechanism. The controller is a discrete-time nonlinear decoupler, which is analyzed both for the adaptive and the fixed parameter cases. A detailed stability analysis is carried out, and the main result is that the closed loop is globally stable and robust with respect to unstructured uncertainty, which may include modeling error and disturbances. In addition, bounds on the asymptotic and transient performance are given. The main assumptions on the system and model are that they must not have strong nonminimum-phase effects, except time-delay, and the unstructured uncertainty must not be too large. A simulation example illustrates some of the properties of the modeling method and model based control structure.<
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