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Dissipativity and stability of interconnections
Author(s) -
Willems Jan C.,
Takaba Kiyotsugu
Publication year - 2006
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.1121
Subject(s) - stability (learning theory) , quadratic equation , differential (mechanical device) , control theory (sociology) , mathematics , dynamical systems theory , computer science , mathematical economics , control (management) , physics , artificial intelligence , thermodynamics , geometry , quantum mechanics , machine learning
A new definition of dissipativity is proposed. It is purely in terms of the rate of supply that goes in and out of a dynamical system. It is proven that dissipativity is equivalent to the existence of a non‐negative storage. Several results regarding the dissipativity of systems defined by quadratic differential forms are given, and some open questions are mentioned. These ideas are applied to the question of stability of interconnected systems. Copyright © 2006 John Wiley & Sons, Ltd.