{'fraction_non_alphanumeric': 0.02280130293159609, 'fraction_numerical': 0.0, 'mean_word_length': 5.275510204081633, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A necessary and sufficient stability criterion for linear time-varying systems

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.