An example is given to show that even if the eigenvalues of the system <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</tex> -matrix <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A(t)</tex> of a linear time-varying system <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ẋ(t) = A(t)x(t)</tex> are independent of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</tex> and some of them have positive real parts, the system is asymptotically stable.
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M. Wu (1974) studied this question.
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