Recently an improved bilinear Routh approximation method has been suggested for the order reduction of discrete systems. In the method, the last $α$ and $β$ parameters of a reduced model were replaced by new parameters so that the impulse response energy of an original system is also preserved in the reduced model without destroying the stability preserving and time-moments matching properties. In this paper a new and simple improvement is proposed from which one can find a suboptimal bilinear Routh approximant. Compared to the previous result, the approach of this paper has an advantage that the improvement is always guaranteed.

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