{'fraction_non_alphanumeric': 0.016536964980544747, 'fraction_numerical': 0.0, 'mean_word_length': 5.638709677419355, '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}}
Output synchronization for heterogeneous networks of discrete-time introspective right-invertible agents with uniform constant communication delay

In this paper, we consider synchronization problems for heterogeneous networks of introspective, right-invertible, discrete-time linear agents with uniform constant communication delay. We first design decentralized controllers for solving the output synchronization problem for a set of network topologies under arbitrary bounded delay. We then apply the proposed scheme to solve the formation problem with arbitrarily given formation vectors. Finally, we consider the output regulation problem, where the output of each agent has to track an a prior specified reference trajectory, generated by an exosystem. In this case, we assume that the common root agent has access to its own output relative to the reference trajectory. We then solve the problem for a set of network topologies with delay whose upper bound depends exosystem and some characteristic of network topologies.