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The present work is concerned with controller design of linear discrete-time systems modeled in the delta domain. Time moment method, a tool so far used for model order reduction is applied to compute online time moments from the input-output response of the plant and reference model to estimate the controller parameters adaptively. Traditionally, discrete-time sampled data systems are represented using shift-operator parameterization. Such parameterizations are not suitable at fast sampling rates. An alternative parameterization using the so-called delta operator maintains a close correspondence to its continuous-time counterpart at fast sampling rate. Using delta operator parameterization it is possible to unify both discrete-time and continuous-time theory. The coefficients of the discrete-time transfer function are similar to the corresponding ones in continuous-time and it becomes easier to tune controller parameters for improved dynamic performance. At fast sampling limit, the delta operator model tends to the analog dynamic system model.