A formal linearization method by the cubic Hermite interpolation for nonlinear systems

2002 ◽  
Author(s):  
K. Narikiyo ◽  
H. Takata
Keyword(s):  
Nonlinear Systems ◽  
Hermite Interpolation ◽  
Linearization Method ◽  
Formal Linearization

scholarly journals On an extension of the stochastic linearization

1993 ◽  
Vol 15 (4) ◽  
pp. 1-6
Author(s):  
Di Paola Mario ◽  
Nguyen Dong Anh
Keyword(s):  
Nonlinear Systems ◽  
Nonlinear Equation ◽  
Random Excitation ◽  
Linearization Method ◽  
Mean Square ◽  
Fundamental Idea ◽  
Stochastic Linearization ◽  
The Mean ◽  
The Difference

Stochastic linearization method is one of the most useful tools for analysis of nonlinear systems under random excitation. The fundamental idea of the classical stochastic linearization consists in replacing the original nonlinear equation by a linear one in such a way that the difference between two equations is minimized in the mean square value. In this paper a new version of the stochastic linearization is proposed. It is shown that for two nonlinear systems considered the new version gives good results for both the weak and strong nonlinearities.

The True Linearization Coefficients for Nonlinear Systems Under Parametric White Noise Excitations

2004 ◽  
Vol 74 (1) ◽  
pp. 161-163 ◽  
Author(s):  
Giovanni Falsone
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Systems ◽  
Nonlinear Response ◽  
Original System ◽  
Linearization Method ◽  
Maximum Likelihood Estimates ◽  
Stationary Case ◽  
Stochastic Linearization ◽  
Linearization Coefficients ◽  
White Noises

In this paper some properties of the stochastic linearization method applied to nonlinear systems excited by parametric Gaussian white noises are discussed. In particular, it is shown that the linearized quantities, obtained by the author in another paper by linearizing the coefficients of the Ito differential rule related to the original system, show the same properties found by Kozin with reference to nonlinear system excited by external white noises. The first property is that these coefficients are the true linearized quantities, in the sense that their exact values are able to give the first two statistical moments of the true response. The second property is that, in the stationary case and in the field of the parameter estimation theory, they represent the maximum likelihood estimates of the linear model quantities fitting the original nonlinear response.

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