Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A theory of nonlinear networks. I

Authors: R. K. Brayton and J. K. Moser
Journal: Quart. Appl. Math. 22 (1964), 1-33
DOI: https://doi.org/10.1090/qam/169746
MathSciNet review: 169746
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Abstract: This report describes a new approach to nonlinear RLC-networks which is based on the fact that the system of differential equations for such networks has the special form

$\displaystyle L\left( i \right)\frac{{di}}{{dt}} = \frac{{\partial P\left( {i,v... ...ht)\frac{{dv}}{{dt}} = - \frac{{\partial P\left( {i,v} \right)}}{{\partial v}}.$

The function, $ P\left( {i,v} \right)$, called the mixed potential function, can be used to construct Liapounov-type functions to prove stability under certain conditions. Several theorems on the stability of circuits are derived and examples are given to illustrate the results. A procedure is given to construct the mixed potential function directly from the circuit. The concepts of a complete set of mixed variables and a complete circuit are defined.

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DOI: https://doi.org/10.1090/qam/169746
Article copyright: © Copyright 1964 American Mathematical Society

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