The generalized frequency response function (GFRF) for Volterra systems described by the nonlinear autoregressive with exogenous input model is determined by a new mapping function based on its parametric characteristic. The -order GFRF can now be directly determined in terms of the first order GFRF, which represents the linear component of the system, and model parameters, which define system nonlinearities. Some new properties of the GFRFs are therefore developed. These results can analytically reveal the linear and nonlinear effects on system frequency response functions, and also demonstrate the relationship between convergence of system Volterra series expansion and model parameters.
1.
Boyd
, S.
, and Chua
, L. O.
, 1985, “Fading Memory and the Problem of Approximating Nonlinear Operators With Volterra Series
,” IEEE Trans. Circuits Syst.
0098-4094, CAS-32
(11
), pp. 1150
–1161
.2.
Sandberg
, W.
, 1982, “Expansions for Nonlinear Systems
,” Bell Syst. Tech. J.
0005-8580, 61
(2
), pp. 159
–199
.3.
Rugh
, W. J.
, 1981, Nonlinear System Theory: The Volterra/Wiener Approach
, The Johns Hopkins University Press
, Baltimore, MD
.4.
Orlowski
P.
2007, “Frequency Domain Analysis of Uncertain Time-Varying Discrete-Time Systems
,” Circuits Syst. Signal Process.
0278-081X, 26
(3
), pp. 293
–310
.5.
Pavlov
, A.
, van de Wouw
, N.
, and Nijmeijer
, H.
, 2007, “Frequency Response Functions for Nonlinear Convergent Systems
,” IEEE Trans. Autom. Control
0018-9286, 52
(6
), pp. 1159
–1165
.6.
Jing
, X. J.
, Lang
, Z. Q.
, and Billings
, S. A.
, 2008, “Output Frequency Response Function Based Analysis for Nonlinear Volterra Systems
,” Mech. Syst. Signal Process.
0888-3270, 22
, pp. 102
–120
.7.
Jing
, X. J.
, Lang
, Z. Q.
, and Billings
, S. A.
, 2009, “Determination of the Analytical Parametric Relationship for Output Spectrum of Volterra Systems Based on Its Parametric Characteristics
,” J. Math. Anal. Appl.
0022-247X, 351
, pp. 694
–706
.8.
George
, D. A.
, 1959, “Continuous Nonlinear Systems
,” MIT Research Laboratory of Electronics, Cambridge, MA, Technical Report No. 355.9.
Peyton-Jones
, J.
, and Billings
, S. A.
, 1989, “Recursive Algorithm for Computing the Frequency Response of a Class of Nonlinear Difference Equation Models
,” Int. J. Control
0020-7179, 50
(5
), pp. 1925
–1940
.10.
Jing
, X. J.
, Lang
, Z. Q.
, and Billings
, S. A.
, 2007, “New Bound Characteristics of NARX Model in the Frequency Domain
,” Int. J. Control
0020-7179, 80
(1
), pp. 140
–149
.11.
Jing
, X. J.
, Lang
, Z. Q.
, Billings
, S. A.
, and Tomlinson
, G. R.
, 2006, “The Parametric Characteristics of Frequency Response Functions for Nonlinear Systems
,” Int. J. Control
0020-7179, 79
(12
), pp. 1552
–1564
.12.
Lang
, Z. Q.
, and Billings
, S. A.
, 1996, “Output Frequency Characteristics of Nonlinear Systems
,” Int. J. Control
0020-7179, 64
(6
), pp. 1049
–1067
.13.
Chen
, S.
, and Billings
, S. A.
, 1989, “Representation of Non-Linear Systems: The NARMAX Model
,” Int. J. Control
0020-7179, 49
, pp. 1012
–1032
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