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In order to simplify the analysis of complex electronic systems, they needsto be modeled accurately. Model reduction is further required to streamline the procedural and computational complexities. Further the instability caused by the model reduction techniques worstly effects the accuracy of a system. Therefore, we have proposed some improvements in the frequency limited impulse response Gramians based model order reduction techniques for discrete time systems. The propsed techniques assures the stability of the model after it get reduced. The proposed techniques provided better results than the stability preserving techniques.