{'fraction_non_alphanumeric': 0.013539651837524178, 'fraction_numerical': 0.0, 'mean_word_length': 5.946308724832215, '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}}
Remarks On The Generalized Lyapunov Operator Spectral Radius Stabilizability Condition in Switched Linear Systems

The generalized Lyapunov operator spectral radius stabilizability condition, which is a sufficient condition for state-feedback exponential stabilizability in discrete-time switched linear systems, is considered and characterized in the present communication. It is shown that a switched linear system obeys the spectral radius stabilizability condition if and only if the considered switched system has a (finite length) transition matrix having spectral radius smaller than one. It is also proved that the satisfaction of the spectral radius stabilizability condition can be characterized in terms of a new (here introduced) sequence associated to the considered switched system. It is moreover shown that the solvability of a new dynamic programming equation, associated to the considered switched system, is a necessary and sufficient condition for the satisfaction of the spectral radius stabilizability condition.