  The dead-zone nonlinearity is frequently encountered in many industrial
automation equipment and its presence can severely compromise control system
performance. Due to the possibility to express human experience in an
algorithmic manner, fuzzy logic has been largely employed in the last decades
to both control and identification of uncertain dynamical systems. In spite of
the simplicity of this heuristic approach, in some situations a more rigorous
mathematical treatment of the problem is required. In this work, an adaptive
fuzzy controller is proposed for nonlinear systems subject to dead-zone input.
The convergence properties of the tracking error will be proven using Lyapunov
stability theory and Barbalat's lemma. An application of this adaptive fuzzy
scheme to a Van der Pol oscillator is introduced to illustrate the controller
design method. Numerical results are also presented in order to demonstrate the
control system performance.
