Abstract: This paper proved the feedback control of δ discrete domain is equal to that one of Z domain under the same closed-loop characteristics.The approximate solution of LQR design using δ operator is obtained.It is proved that when the sampling interval T→0 the optimal gain using δ operator approximates to that one of its continuous system under the same quadratic cost function and can be solved directly by the con- tinuous Riccati equation.The closed-loop characteristics of systems using δ operator are also more close to that ones of the continuous systems than using Z operator.An example is used to compare these methods and verify the above results.