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Models of dynamical systems become increasingly complex. While this allows a more accurate description of the underlying process, it often renders the application of model-based control algorithms infeasible. In this paper, we propose a model reduction procedure for systems described by nonlinear ordinary differential equations. The reduced model used to approximate the input-output map of the system is parameterized via the observability normal form. To preserve the steady states of the system and their stability properties, the set of feasible parameters of the reduced model has to be constrained. Therefore, we derive necessary and sufficient conditions for simultaneous exponential stability of a set of steady states of the nonlinear reduced model. The local approximation of these constraints results in a sequential convex program for computing the optimal parameters. The proposed approach is evaluated using the Fermi-Pasta-Ulam model.