Considering that the controller parameters are of additive norm-bounded uncertainties when realized,a design method of robust non-fragile H-infinity controller for uncertain systems based on Delta operator theory is illustrated in this paper.A sufficient and necessary condition of the existence for the controller is given,which is presented in LMI forms.Finally,the designed method is used in the speed control system of a permanent magnet linear synchronous motor (PMLSM).With the designed controller,the resulting speed closed-loop system is still stable and has the expected Hinfinity performance even if the sample period is reduced and the parameters of the controller and the controlled object are varied.The results show that the designed method is effective.