{'fraction_non_alphanumeric': 0.00980392156862745, 'fraction_numerical': 0.0016339869281045752, 'mean_word_length': 5.5212765957446805, '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}}
A nonlinear full order observer for oscillator tracking

We present a class of nonlinear observers that track oscillator states from observations of the complex envelope. We first identify core state variables that are observable and provide a general observer structure for estimating these state variables, that results in globally uniformly asymptotically stable observers. We provide a specialization that induces the 2-norm of the state estimation error to monotonically decline to zero, and has an intuitively appealing structure that has parallels to full order observers of Linear Time Invariant systems.