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Linear matrix inequalities for analysis and control of linear vector second‐order systems
Author(s) -
Adegas F. D.,
Stoustrup J.
Publication year - 2014
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.3242
Subject(s) - lyapunov function , mathematics , matrix (chemical analysis) , linear matrix inequality , order (exchange) , control theory (sociology) , stability (learning theory) , stability theory , dynamical systems theory , linear system , linear dynamical system , control (management) , mathematical optimization , computer science , mathematical analysis , nonlinear system , materials science , physics , finance , quantum mechanics , artificial intelligence , machine learning , economics , composite material
Summary Many dynamical systems are modeled as vector second‐order differential equations. This paper presents analysis and synthesis conditions in terms of LMI with explicit dependence in the coefficient matrices of vector second‐order systems. These conditions benefit from the separation between the Lyapunov matrix and the system matrices by introducing matrix multipliers, which potentially reduce conservativeness in hard control problems. Multipliers facilitate the usage of parameter‐dependent Lyapunov functions as certificates of stability of uncertain and time‐varying vector second‐order systems. The conditions introduced in this work have the potential to increase the practice of analyzing and controlling systems directly in vector second‐order form. Copyright © 2014 John Wiley & Sons, Ltd.