Abstract
This paper presents a method of the determination of the steady state response for a class of nonlinear systems. The response of a nonlinear system to a given input is first obtained in the form of a series solution in the multidimensional frequency domain. Conditions are then determined for which this series solution will converge. The conversion from multidimensions to a single dimension is then made by the method of association of variables, and thus an equivalent linear model of the nonlinear system is obtained. The steady state response is then found by any technique employed with linear system.
Keywords
MathematicsNonlinear systemSteady state (chemistry)Series (stratigraphy)Control theory (sociology)Frequency responseDimension (graph theory)Applied mathematicsClass (philosophy)State (computer science)Computer scienceAlgorithmEngineering
Affiliated Institutions
Related Publications
Pumping conditions for parametric gain with a nonlinear immittance element
The necessary conditions for parametric amplification obtained by Penfield for the series nonlinear capacitive-linear resistive element are extended to the case when the resisti...
Optimization of time-varying systems
A method of self-optimization using system models to compute error-criterion gradients in a parameter space is extended to time-varying systems. When the parameters are permitte...
Modern Control Engineering
From the Publisher: This comprehensive treatment of the analysis and design of continuous-time control systems provides a gradual development of control theory—and shows how to...
Nonlinear decoupling via feedback: A differential geometric approach
The paper deals with the nonlinear decoupling and noninteracting control problems. A complete solution to those problems is made possible via a suitable nonlinear generalization...
Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions
The Nelder--Mead simplex algorithm, first published in 1965, is an enormously popular direct search method for multidimensional unconstrained minimization. Despite its widesprea...
Publication Info
- Year
- 1980
- Type
- article
- Volume
- 3
- Issue
- 3
- Pages
- 535-547
- Citations
- 4
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
4
OpenAlex
Cite This
Sudhangshu B. Karmakar
(1980).
Steady state response of a nonlinear system.
International Journal of Mathematics and Mathematical Sciences
, 3
(3)
, 535-547.
https://doi.org/10.1155/s0161171280000403
Identifiers
- DOI
- 10.1155/s0161171280000403