Comments on "Vector norms as Lyapunov functions for linear systems" [with reply]

The purpose of this note is to give a counterexample to a possible implication of the main result of the above paper by Kiendl-Adamy-Stelzner (ibid., vol.37, no.6, p.839-42 (1992)), to modify this result, to restate its theorem accordingly, and to supply a proof for it. In reply, Kiendl et al. point out that they did not formulate the condition as necessary for a vector norm being a Lyapunov function. Due to Hmamed´s remarks, they have reviewed their statements for imprecise formulations.<>