As pointed out by Professor Khalil Ezzinbi, in Lemma 3.3 on p. 1720, the claim that the existence of a bounded solution on ℝ of Equation (11) implies that G has no eigenvalues with null real part, so there exists a bounded solution of Equation (11) on ℝ is false. One can easily construct many examples with matrix G having eigenvalues with null real parts and Equation (11) has a bounded solution on ℝ. We have been unable to overcome this difficulty in a meaningful way. It should be pointed out that if it furthermore requires that matrix G has no eigenvalues with null part, the conclusion of Lemma 3.3 is correct. Note that matrix G is already defined above, the requirement is unreasonable.
We are grateful to Prof. Khalil Ezzinbi for pointing out the mistake and apologize to the readers for these errors.