Generalized frequency response function matrix for MIMO non-linear systems

Recursive algorithms are derived to compute the generalized frequency response function matrix of multi-input multioutput (MIMO) non-linear systems as an analytical map from both non-linear differential equation models and NARX (Non-linear Auto Regressive Models with eXogenous inputs) models of the system. The algorithm is computationally compact and exposes the explicit relationship between the model parameters and the elements of the generalized frequency response function matrix and can thus provide important insights into the behaviour of non-linear systems.

[1]  Y. W. Lee,et al.  Measurement of the Wiener Kernels of a Non-linear System by Cross-correlation† , 1965 .

[2]  E. Bedrosian,et al.  The output properties of Volterra systems (nonlinear systems with memory) driven by harmonic and Gaussian inputs , 1971 .

[3]  K. Naka,et al.  Identification of multi-input biological systems. , 1974, IEEE transactions on bio-medical engineering.

[4]  Lawrence Stark,et al.  Kernel method for nonlinear analysis: identification of a biological control system , 1975 .

[5]  L. Stark,et al.  The kernel identification method (1910–1977)— review of theory, calculation, application, and interpretation , 1977 .

[6]  L. Chua,et al.  Frequency domain analysis of nonlinear systems: general theory , 1979 .

[7]  Stephen A. Billings,et al.  Identi cation of nonlinear systems-A survey , 1980 .

[8]  R. D. Figueiredo.  The Volterra and Wiener theories of nonlinear systems , 1982 .

[9]  R. de Figueiredo.  The Volterra and Wiener theories of nonlinear systems , 1982, Proceedings of the IEEE.

[10]  Edward J. Powers,et al.  A digital method of modeling quadratically nonlinear systems with a general random input , 1988, IEEE Trans. Acoust. Speech Signal Process..

[11]  S. Billings,et al.  Recursive algorithm for computing the frequency response of a class of non-linear difference equation models , 1989 .

[12]  S. Billings,et al.  Mapping non-linear integro-differential equations into the frequency domain , 1990 .

[13]  D. Linebarger,et al.  Estimating transfer functions of quadratically nonlinear systems , 1991, [1991] Conference Record of the Twenty-Fifth Asilomar Conference on Signals, Systems & Computers.

[14]  S. Billings,et al.  Frequency response functions for nonlinear rational models , 1995 .

[15]  Edward J. Powers,et al.  Identification of cubic systems using higher order moments of i.i.d. signals , 1995, IEEE Trans. Signal Process..

[16]  Hai-Wen Chen,et al.  Modeling and identification of parallel nonlinear systems: structural classification and parameter estimation methods , 1995, Proc. IEEE.