In this paper we propose an approximated method for the design of feedforward actions based on model stable inversion. In the proposed framework the solution of the model stable inversion is approximated in the least squares sense by a suitable combination of any arbitrary set of basis functions. The paper makes use of operator theory to derive a closed-form formula to compute such approximation and to provide boundedness properties for the computed solution. Simulations are provided to show the effectiveness of the proposed method with different families of basis functions. (C) 2018 Elsevier Ltd. All rights reserved.