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Uniqueness of the steady state for small source amplitudes in non‐linear non‐autonomous circuitsc
Author(s) -
Hasler Martin,
Verburgh Philippe
Publication year - 1985
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.4490130103
Subject(s) - uniqueness , passivity , bounded function , mathematics , voltage source , control theory (sociology) , resistive touchscreen , steady state (chemistry) , state (computer science) , amplitude , capacitor , topology (electrical circuits) , port (circuit theory) , electronic circuit , inductor , mathematical analysis , voltage , computer science , physics , control (management) , combinatorics , electronic engineering , electrical engineering , engineering , chemistry , algorithm , quantum mechanics , artificial intelligence , computer vision
The purpose of this paper is to give a sufficient condition for the uniqueness of the steady state for circuits that are composed of strictly locally passive capacitors and inductors, of time‐dependent bounded voltage and current sources and of a resistive N‐port that is strictly locally passive and eventually strictly passive. It is an extension of previously obtained results by the same authors, where strong local passivity was required. the new condition allows one to give a bound on the source amplitudes below which passive elements. It also gives a more explicit content to a theorem by Chua and Green which states that for sufficiently small source amplitudes the steady state is unique. the new condition is obtained by giving explicit uniform eventual bounds on the solutions as t → ∞, which are of independent interest. Two examples illustrate that the various explicit bounds can easily be computed in concrete examples.