{'fraction_non_alphanumeric': 0.019230769230769232, 'fraction_numerical': 0.0, 'mean_word_length': 5.331081081081081, '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}}
Global extension of local control Lyapunov functions via exit-time optimal control *

This paper studies the feedback stabilization problem for deterministic nonlinear control systems described by ODEs. Assuming that a local control Lyapunov function (CLF) with certain properties can be explicitly constructed, we propose a way of extending it to a global CLF. Under a number of reasonable conditions, it is proved that the concatenation of the local CLF and the value function for an appropriately formulated exit-time optimal control problem leads to a global CLF satisfying the sought-after infinitesimal decrease property. The exit-time problem is stated with respect to a sublevel set of the local CLF. We then develop the theoretical foundations of a curse-of-dimensionality-free characteristics based approach for approximating the related value function. Future research directions and possible applications are also discussed.