A note on stability conditions for planar switched systems

This article is concerned with the stability problem for the planar linear switched system [image omitted], where the real matrices A1, A2 22 are Hurwitz and u() : [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(). 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]. © 2009 Taylor & Francis.