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Nonlinear stochastic passivity, feedback equivalence and global stabilization
Author(s) -
Lin Zhongwei,
Liu Jizhen,
Lin Yan,
Zhang Weihai
Publication year - 2012
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.1742
Subject(s) - passivity , nonlinear system , equivalence (formal languages) , control theory (sociology) , lemma (botany) , minimum phase , mathematics , class (philosophy) , computer science , control (management) , phase (matter) , engineering , discrete mathematics , physics , ecology , poaceae , quantum mechanics , artificial intelligence , electrical engineering , biology
SUMMARY This paper addresses several important issues including stochastic passivity, feedback equivalence and global stabilization for a class of nonlinear stochastic systems. Based on a nonlinear stochastic Kalman–Yacubovitch–Popov (KYP) lemma, we investigate the relationship between a stochastic passive system and the corresponding zero‐output system. Different from the deterministic case, it is shown for the first time that feedback equivalence to a stochastic passive system requires a strong minimum‐phase condition, not the minimum‐phase one. Following the stochastic passivity theory, global stabilization results are established for a class of nonlinear stochastic systems with relative degree 1≤ r < n . An example is presented to illustrate the effectiveness of our results. Copyright © 2011 John Wiley & Sons, Ltd.