{'fraction_non_alphanumeric': 0.02118270079435128, 'fraction_numerical': 0.0, 'mean_word_length': 4.968421052631579, '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}}
Using the Superposition Property for Model Reduction of Linear Systems with a Large Number of Inputs

At present, almost all model order reduction methods assume single-input single-output (SISO) systems or systems with a small number of inputs and outputs. Few methods can deal with systems with a large number of inputs and outputs. Multi-input multi-output (MIMO) systems appear for example in modeling of integrated circuits. The number of inputs and outputs sometimes is very large, even close to the number of state variables. In this paper we propose a novel model reduction technique which can efficiently perform model reduction for linear systems with a large number of inputs and outputs. Motivated by the superposition property of linear systems, model order reduction is performed separately with respect to each column of the input matrix. Then, the output response of the original multi-input system is approximated by the summation of the output responses of the reduced-order single-input systems corresponding to each column of the input matrix. The proposed method applies to both multi-input single-output systems