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Asymptotic stability of interconnected passive non‐linear systems
Author(s) -
Isidori A.,
Joshi S. M.,
Kelkar A. G.
Publication year - 1999
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/(sici)1099-1239(19990430)9:5<261::aid-rnc403>3.0.co;2-v
Subject(s) - passivity , linear system , exponential stability , interconnection , control theory (sociology) , property (philosophy) , class (philosophy) , mathematics , lti system theory , invariant (physics) , stability (learning theory) , linear control systems , stability theory , computer science , nonlinear system , mathematical analysis , control (management) , engineering , telecommunications , physics , philosophy , epistemology , quantum mechanics , artificial intelligence , machine learning , electrical engineering , mathematical physics
This paper addresses the problem of stabilization of a class of internally passive non‐linear time‐invariant dynamic systems. A class of non‐linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input‐strictly passive systems. It is shown that the interconnection of a non‐linear passive system and a non‐linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input‐strictly passive. In the case of linear time‐invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check. Copyright © 1999 John Wiley & Sons, Ltd.