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A possibility of filling the gap between local and global passivity of non‐linear networks and some of its consequences
Author(s) -
Roska Tamás
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.4490090404
Subject(s) - diagonally dominant matrix , passivity , mathematics , class (philosophy) , monotone polygon , reciprocity (cultural anthropology) , diagonal , stability (learning theory) , topology (electrical circuits) , pure mathematics , discrete mathematics , invertible matrix , mathematical optimization , computer science , combinatorics , geometry , psychology , social psychology , electrical engineering , artificial intelligence , machine learning , engineering
In the qualitative theory of non‐linear networks the non‐linear n ‐ports are generally considered either locally passive or globally passive even eventually globally passive (the most restrictive or the least restrictive properties respectively). Moreover the reciprocity condition in many cases (e.g. complete stability) restricts the area of applications. In the area of economics and other fields, basically motivated by Sandberg's results, the role of the off‐diagonally monotone and antitone mappings is crucial. In this paper, based on the above facts and results, it is shown that partly similar classes of mappings could have a role in non‐linear network theory. More precisely, the off‐diagonally locally active (passive) n ‐ports, defined in the paper, could represent an important new class of n ‐ports. As an application of the features of this new class of n ‐ports two Theorems are given showing conditions under which in case of a network consisting of off‐diagonally locally active n ‐ports the DC solution can be uniquely calculated using the standard iterative methods and an autonomous network is asymptotically stable in a given domain. Hence, this paper partially overcomes the so called ‘curse of non‐reciprocity’.