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Necessary and sufficient conditions for absolute stability of linear n ‐ports
Author(s) -
Zeheb Ezra,
Walach Eugene
Publication year - 1981
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490090306
Subject(s) - bibo stability , stability (learning theory) , mathematics , set (abstract data type) , control theory (sociology) , matrix (chemical analysis) , zero (linguistics) , mathematical analysis , topology (electrical circuits) , computer science , combinatorics , nonlinear system , physics , machine learning , artificial intelligence , composite material , programming language , linguistics , philosophy , materials science , control (management) , quantum mechanics
A set of necessary and sufficient conditions is stated and proved for the absolute stability (under any passive terminations), in the ‘bibo’ sense, of a linear n ‐port characterized by its open‐circuit impedance matrix. A more explicit set of such conditions is derived for the special case n = 3. In the process of deriving this set of conditions, some results and theorems concerning finding the zero sets of two and three parameter functions, are stated and proved. Also derived is a set of necessary and sufficient conditions for the absolute stability of two‐ports characterized by the scattering parameters. Such sets have already been derived previously, but the present set is considerably simpler.