In this paper a necessary and sufficient exponential stability criterion is presented for linear time-varying (LTV) systems based on a previously developed parallel D-spectrum concept. This new result is a corrected version of some previously published results, where an important condition has been overlooked. Extensions of the new result to the assessment of exponential stability using a series D-spectrum, and the assessment of asymptotic stability using a relative-mean concept for the PD- and SD-eigenvalues are also discussed.
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Jianjun Zhu (2002) studied this question.