Abstract
This article considers the question of existence and uniqueness of the response of nonlinear time-varying RLC networks driven by independent voltage and current sources. It is proved that under certain conditions the response exists, is unique, and is defined by a set of ordinary differential equations satisfying some Lipschitz conditions. These conditions are of two types: (1) the network elements must have characteristics which satisfy suitable Lipschitz conditions and (2) the network must satisfy certain topological conditions. It should be noted that elements with nonmonotonic characteristics are allowed and that the element characteristics need to be continuous but not differentiable.
Keywords
RLC circuitUniquenessLipschitz continuityNonlinear systemMathematicsOrdinary differential equationDifferentiable functionControl theory (sociology)Topology (electrical circuits)Set (abstract data type)VoltageMathematical analysisApplied mathematicsDifferential equationComputer scienceEngineeringPhysicsCombinatorics
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Publication Info
- Year
- 1965
- Type
- article
- Volume
- 44
- Issue
- 1
- Pages
- 161-198
- Citations
- 68
- Access
- Closed
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Cite This
C. Desoer,
J. Katzenelson
(1965).
Nonlinear RLC Networks.
Bell System Technical Journal
, 44
(1)
, 161-198.
https://doi.org/10.1002/j.1538-7305.1965.tb04141.x
Identifiers
- DOI
- 10.1002/j.1538-7305.1965.tb04141.x