{'fraction_non_alphanumeric': 0.04449152542372881, 'fraction_numerical': 0.006355932203389831, 'mean_word_length': 4.031914893617022, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 1, '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}}
Exponential stabilization of 1-d wave equation with input delay

Abstract: In this paper, we consider the stabilization problem of 1-d wave equation with input delay. Suppose that the wave system is fixed at one end whereas a control force is applied at other end. Here we consider the control force of the form αu(t) + βu(t − τ) where τ is the time delay. In this paper we find a feedback control law that stabilizes exponentially the system for any |α| ̸= |β| and τ > 0.