$H_{\infty}$ control for uncertain T-S fuzzy systems

This paper investigates the
$H_{\infty}$
control problem for nonlinear systems with uncertainties and disturbances. Firstly, T-S fuzzy models are utilized to approximate the nonlinear systems. Then, an fuzzy control scheme with an adaptive mechanism is developed to compensate the effect of the uncertainties on the systems. In addition, to reduce the influence of the disturbance and further improve the performance of
$H_{\infty}$
control, an adaptive membership function-dependent
$H_{\infty}$
performance index is considered and the corresponding analysis conditions are obtained. Finally, a numerical example for 2-order systems is presented to show the advantage of the presented approach with the above-mentioned performance index.