Abstract:The problem of P and PI feedback control to a time delay system was investigated,with the emphasis on the determination of the feedback gains that ensured the asymptotical stability of the delayed system. By means of Lambert W function,the feedback gain of P control can be expressed explicitly,so that the optimal feedback gain can be easily obtained. For the system under a PI control,the stable region of the feedback gains was determined on the basis of stability switches and Dsubdivision,and the optimal feedback gains that enabled the system to admit maximal stable margin were figured out numerically by using Lambert W function. From the viewpoint of computation,the present method is much simpler than the available methods.