{'fraction_non_alphanumeric': 0.011345218800648298, 'fraction_numerical': 0.0, 'mean_word_length': 5.645161290322581, '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}}
Minimum Number of Controls for Full Controllability of Linear Time-Invariant Systems

For linear stationary system a new controllability analysis technique is introduced. This concept is closely related to determination of minimum number of independent controls necessary for complete controllability. This process consist in transforming the original system into Frobenius normal form. We show that there are no fewer controls that achieve full controllability of the system. Furthermore, the Frobenius normal form is presented as a mathematical advantage in the design of control matrices for underactuated systems.