{'fraction_non_alphanumeric': 0.017432646592709985, 'fraction_numerical': 0.0, 'mean_word_length': 5.515463917525773, '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}}
Stabilization of nonlinear systems by adding state-dependent rough signals

This paper provides a stabilization strategy for input-affine systems by adding state-dependent rough signals, a particular kind of continuous processes having unbounded variations. The effective use of rough path analysis enables state-feedbacks to gain entrance to the mechanism of rough signals. The results demonstrate that the addition of rough signals also invocates “hidden control inputs” that make the systems controllable using Lie derivatives. This implies that control Lie algebra can be constructed by Lie derivatives instead of Lie brackets.