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A new small‐gain theorem with an application to the stabilization of the chemostat
Author(s) -
Karafyllis Iasson,
Jiang ZhongPing
Publication year - 2011
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.1773
Subject(s) - small gain theorem , chemostat , control theory (sociology) , stability (learning theory) , property (philosophy) , nonlinear system , high gain antenna , transient (computer programming) , mathematics , computer science , engineering , control (management) , physics , philosophy , epistemology , quantum mechanics , machine learning , artificial intelligence , biology , bacteria , electrical engineering , genetics , operating system
SUMMARY New small‐gain results are obtained for nonlinear feedback systems under relaxed assumptions. Specifically, during a transient period, the solutions of the feedback system may not satisfy some key inequalities that previous small‐gain results usually utilize to prove stability properties. The results allow the application of the small‐gain perspective to various systems that satisfy less‐demanding stability notions than the input‐to‐output stability property. The robust global feedback stabilization problem of an uncertain time‐delayed chemostat model is solved by means of the new small‐gain results. Copyright © 2011 John Wiley & Sons, Ltd.