{'fraction_non_alphanumeric': 0.01731244847485573, 'fraction_numerical': 0.0, 'mean_word_length': 5.322916666666667, '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}}
Analysis of pulse width modulation controlled systems based on a piecewise affine description

The problem of assuring the asymptotic stability of a pulse width modulation (PMW) control scheme is a classical topic in control engineering, where a continuous‐time control signal is approximated by a piecewise constant signal. This paper proposes a general framework that either shows the local asymptotic stability of the closed‐loop PWM system or proves the convergence of the state to an invariant set, which is the case in the presence of limit cycles. The proposed method is based on a piecewise affine representation of the closed‐loop system in discrete time, and it uses semidefinite programming both to find a Lyapunov‐like function and to determine an estimate of the region of attraction. This is an important feature since the desired continuous‐time control action at some instants may be larger than the magnitude of the PWM signals, leading to saturation of the applied control action, a well‐known source of performance degradation and even instability. Two academic examples of applications are shown, in the domain of spacecraft positioning control and electric direct current (DC) motor servoing.