{'fraction_non_alphanumeric': 0.0231023102310231, 'fraction_numerical': 0.0, 'mean_word_length': 6.226190476190476, '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}}
Existence of parameter-dependent Lyapunov functions assuring robust stability via SOS

An SOS relaxation technique seeking homogeneous polynomially parameter dependent (HPPD) Lyapunov function to non-quadratic stability is proposed. We investigate non-quadratic relaxed conditions characterized by sum of squares, exploiting the algebraic property of Po´lya Theorem to construct a family of finite-dimensional SOS relaxations that releases conservatism without adding any slack matrices. Lastly, numerical experiments to illustrate the advantage of the relaxation, being simple and effective, are provided.