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Determining input‐to‐state and incremental input‐to‐state stability of nonpolynomial systems
Author(s) -
Voßwinkel Rick,
Röbenack Klaus
Publication year - 2020
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.5012
Subject(s) - constructive , state (computer science) , stability (learning theory) , decomposition , property (philosophy) , polynomial , mathematics , computer science , mathematical optimization , control theory (sociology) , algorithm , control (management) , artificial intelligence , process (computing) , ecology , mathematical analysis , philosophy , epistemology , machine learning , biology , operating system
Summary In this study, we propose constructive ways to determine input‐to‐state stability (ISS) as well as incremental ISS ( δ ISS) of nonpolynomial dynamical systems. The developed procedures are based on sums‐of‐square decomposition. This tool is only applicable to polynomial systems. Thus, a rational recast of the nonpolynomial system description is used. This recast generally leads to an increased system order and additional constraints. These constraints must be respected in the resulting formulations. The proposed approach gives a unique and constructive procedure to determine the ISS and the δ ISS property, which is normally nontrivial and needs a good understanding of the system's dynamics. The proposed approaches are illustrated on several examples.