The economic simulation design problem is that given performance requirements, design the simulation of a linear system and distribute precision among the instruments such that the computational cost is minimized without violating the simulation accuracy. In this paper, we consider the simulation of a large-scale linear system in digital devices with fixed-point arithmetic and finite wordlength. Given the output variance upperbound, we focus on finding an optimal realization and the allocation

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... f wordlength among A/D converter, computer and sensors. This problem is in general not convex because of the scaling constraint. By exploring the special structure of this joint optimization problem and under reasonable assumptions, we simplify this problem and find the optimal coordinate transformation and the wordlength allocation scheme simultaneously by solving LMIs (linear matrix inequalities). Numerical results are given which compare this new realization with the balanced realization and random realizations.