The stability is considered of a repetitively switched system described by a finite number of linear differential equations periodically iterated in fixed order. Some new results that characterize the dependence of the system stability upon the switching frequency are presented. Some of these results are immediately applicable to the stability analysis of sampled data systems. Our approach to the.question, which is based on the Baker-Campbell-Hausdorff formula and on known theorems on localization on the complex plane of eigenvalues of a matrix, has a simple geometric interpretation and allows the provision of qualitative as well as quantitative stability conditions for the system.