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Low frequency Lagrange stabilization for pendulum‐like systems
Author(s) -
Li Peng,
Wang Yijing,
Zuo Zhiqiang
Publication year - 2021
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5512
Subject(s) - control theory (sociology) , lemma (botany) , frequency domain , pendulum , linear matrix inequality , norm (philosophy) , mathematics , controller (irrigation) , inverted pendulum , stability (learning theory) , lagrange multiplier , domain (mathematical analysis) , computer science , mathematical optimization , control (management) , engineering , mathematical analysis , nonlinear system , physics , mechanical engineering , ecology , agronomy , poaceae , quantum mechanics , artificial intelligence , machine learning , law , political science , biology
In this article, the low frequency Lagrange stabilization issue is investigated for a pendulum‐like system. To this end, an H ∞ control method is developed for converting the frequency‐domain stabilization condition into an H ∞ norm bound requirement in low frequency domain. With the aid of a generalized Kalman‐Yakubovich‐Popov (KYP) lemma, time‐domain matrix inequality conditions are derived to assure both pendulum‐like and low frequency Lagrange stability properties for the closed‐loop system. Furthermore, an output feedback Lagrange stabilization controller is constructed via feasible solutions of a certain set of linear matrix inequalities. An illustrative example is provided to verify the effectiveness and superiority of the proposed controller.