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Algebraic and geometric properties of equilibria in cyclic switched dynamic systems
Author(s) -
Becerra Gerardo,
Patino Diego,
Minh Tu Pham,
LinShi Xuefang
Publication year - 2016
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.3679
Subject(s) - algebraic number , mathematics , state space , algebraic equation , real algebraic geometry , set (abstract data type) , algebraic geometry , computer science , pure mathematics , algebra over a field , mathematical analysis , physics , nonlinear system , statistics , programming language , quantum mechanics
Summary The analysis of some properties for the equilibria of switched dynamic systems is addressed. In particular, the geometric properties of the equilibrium region in state space and the algebraic properties of the equations defining it are studied. Based on fundamental results from algebraic geometry, the equilibria properties of switched dynamic systems are analyzed. This alternative approach allows to obtain information about the set of equilibrium points without explicitly computing it. This study is developed for three different formulations of switched dynamic systems, revealing some interesting algebraic and geometric relations in their corresponding equilibria. Some examples, including the case of a power converter, are presented for illustration purposes. Copyright © 2016 John Wiley & Sons, Ltd.