{'fraction_non_alphanumeric': 0.03914590747330961, 'fraction_numerical': 0.0, 'mean_word_length': 5.865853658536586, '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}}
Stochastic stability with S-eigenvalues in stochastic systems

This paper deals with an S-stability (stochastic-stability) using an S-eigenvalue (stochastic-eigenvalue) concept in the linear time-invariant stochastic system where a stochastic mode in dynamics depends on stochastic uncertainties. Our main contributions include the proposition of the S-stability concept for S-eigenvalue, S-eigenvector (stochastic-eigenvector) and its PDF (probability density function) in the complex plane. Numerical examples are presented to illustrate the proposed concepts.