This article is concerned with the stability problem for the planar linear switched system [image omitted], where the real matrices A1, A2 2x2 are Hurwitz and u(center dot) : [0, [ {0, 1} is a measurable function. We give coordinate-invariant necessary and sufficient conditions on A1 and A2 under which the system is asymptotically stable for arbitrary switching functions u(center dot). The new conditions unify those given in previous papers and are simpler to be verified since we reduced to study 4 cases instead of 20. Most of the cases are analysed in terms of the function [image omitted].