{'fraction_non_alphanumeric': 0.017964071856287425, 'fraction_numerical': 0.0, 'mean_word_length': 5.275, '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}}
On discrete time nonnegative storage functions and state functions

We study discrete time dissipativeness. Particularly, we focus on storage functions. Different from the continuous time case, every storage function is not necessarily a state function in discrete time. For this problem, we show that every nonnegative storage function is a state function in discrete time. In addition, we provide some of the necessary and sufficient conditions for the existence of the nonnegative storage function.