Spectral balance: a frequency domain framework for analysis of nonlinear dynamical systems

2004 ◽  
Author(s):  
A. Banaszuk ◽  
P.G. Mehta ◽  
I. Mezic
Keyword(s):  
Dynamical Systems ◽  
Frequency Domain ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
Spectral Balance

Frequency domain conditions for the robust stability of linear and nonlinear dynamical systems

1991 ◽  
Vol 38 (4) ◽  
pp. 389-397 ◽  
Author(s):  
S. Dasgupta ◽  
P.J. Parker ◽  
B.D.O. Anderson ◽  
F.J. Kraus ◽  
M. Mansour
Keyword(s):  
Dynamical Systems ◽  
Frequency Domain ◽  
Robust Stability ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
Linear And Nonlinear

scholarly journals NOISE IMMUNITY RESEARCH FOR NONLINEAR DYNAMICAL SYSTEMS IDENTIFICATION BASED ON VOLTERRA MODEL IN FREQUENCY DOMAIN

2014 ◽  
pp. 34-41
Author(s):  
Vitaliy Pavlenko ◽  
Sergei Pavlenko ◽  
Viktor Speranskyy
Keyword(s):  
Dynamical Systems ◽  
Frequency Domain ◽  
Noise Immunity ◽  
Nonlinear Dynamical Systems ◽  
Interpolation Method ◽  
Test System ◽  
Volterra Model ◽  
Third Order ◽  
Nonlinear Dynamical ◽  
Systems Identification

The accuracy and noise immunity of the interpolation method of nonlinear dynamical systems identification based on the Volterra model in the frequency domain is studied in this paper. The polyharmonic signals are used for the testing the method. The algorithmic and software toolkit in Matlab is developed for the identification procedure. This toolkit is used to construct the informational models of test system and communication channel. The model is built as a first-, second- and third-order amplitude–frequency and phase–frequency characteristics. The comparison of obtained characteristics with previous works is given. Wavelet denoising is studied and applied to reduce measurement noise.

Error Estimation of Fourier Series Expansion and Implication to Solution Accuracy for Nonlinear Dynamical Systems

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Y. M. Chen ◽  
Z. R. Lv ◽  
J. K. Liu
Keyword(s):  
Fourier Series ◽  
Dynamical Systems ◽  
Frequency Domain ◽  
Error Estimation ◽  
Series Expansion ◽  
Nonlinear Dynamical Systems ◽  
Frequency Domain Analysis ◽  
Fourier Series Expansion ◽  
Nonlinear Dynamical ◽  
Time Points

Fourier series expansion (FSE) plays a pivotal role in frequency domain analysis of a wide variety of nonlinear dynamical systems. To the best of our knowledge, there are two general approaches for FSE, i.e., a collocation method (CM) previously proposed by the authors and the classical discrete FSE. Though there are huge applications of these methods, it still remains much less understood in their relationship and error estimation. In this study, we proved that they are equivalent if time points are uniformly chosen. Based on this property, more importantly, the error was analytically estimated for both discrete Fourier expansion (DFE) and CM. Furthermore, we revealed that the accuracy of frequency domain solutions cannot be improved by increasing the number of time points alone, whereas it absolutely depends upon the truncated number of harmonics. It indicates that an appropriate number of time points should be chosen in FSE if frequency domain solutions are targeted for nonlinear dynamical systems, especially those with complicated functions.

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