SUMMARY The main aspect of this paper is to show that the stability of linear time-variant systems cannot be estimated from the location of the eigenvalues. For this purpose, two simple time-variant electrical circuits are presented, which have constant eigenvalues. As will be shown, the time-variant circuits can be asymptotically stable although there is a positive eigenvalue and this circuit can be unstable despite negative eigenvalues only. The idea behind is a suited time-variant state transformation of a linear time-invariant system. An electrical interpretation of both systems and of state transformations allows for an energetic evaluation from an electrical point of view even though the analytical solution is not necessarily known. Copyright (c) 2012 John Wiley & Sons, Ltd.