In this paper, we consider the estimation and variable selection problem for partially linear additive spatial autoregressive models (PLASARM). We propose a robust estimation of two-stage Walsh-average regression (2SWAR) based on Walsh-average regression and instrumental variable method. Under some mild conditions, we obtain and theoretically prove the asymptotic normality of finite parameter vectors and the convergence rate of the nonparametric part. In addition, We also propose a robust variable selection method and further demonstrate its ability to consistently identify real models. We further carry out Monte Carlo simulation and real data analysis, both of which yield promising numerical results.