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Further comments on "Vector norms as Lyapunov functions for linear systems"

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3 Author(s)
Loskot, K. ; Inst. of Math., Silesian Univ., Katowice, Poland ; Polanski, A. ; Rudnicki, R.

This paper deals with the conditions for a vector norm to be a Lyapunov function for a linear time-invariant system. An error in the proof of the related theorem given in Hmamed (1994) is pointed out, and a counterexample proving that this theorem is generally false is provided. It is demonstrated that the considered problem is related to the one of extending a linear operator without increasing its norm.

Published in:

Automatic Control, IEEE Transactions on  (Volume:43 ,  Issue: 2 )