{'fraction_non_alphanumeric': 0.012844036697247707, 'fraction_numerical': 0.0, 'mean_word_length': 5.5, '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}}
Fractional representation theory: Robustness results with applications to finite dimensional control of a class of linear distributed systems

This paper reviews and extends fractional representation theory. In particular, new and powerful robustness results are presented. This new theory is utilized to develop a preliminary design methodology for finite dimensional control of a class of linear evolution equations on a Banach space. We design for stability in an input-output sense but pay particular attention to internal stability as well.