A possibility of filling the gap between local and global passivity of non‐linear networks and some of its consequences

摘要

AbstractIn the qualitative theory of non‐linear networks the non‐linearn‐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 ofn‐ports.As an application of the features of this new class ofn‐ports two Theorems are given showing conditions under which in case of a network consisting of off‐diagonally locally activen‐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 ‘cu