Matrix analysis of mildly nonlinear, multiple-input, multiple-output systems with memory

A matrix method of analysis is developed for mildly nonlinear, multiple-input, multiple-output systems with memory (e.g., nonlinear multiport networks and multichannel communication systems). The method is based on a Volterra-series representation whose kernels are two-dimensional matrices rather than multidimensional arrays. This is made possible through the use of the Kronecker product of matrices, which results in a compact formulation. The response of the aforementioned systems to multiple sinusoidal excitations is also studied. Moreover, formulas are given for various system operations (e.g., addition, cascading, inversion, and feedback), which can be used to describe a complex system as an interconnection of simple subsystems.

[1]  I. W. Sandberg,et al.  Expansions for nonlinear systems , 1982, The Bell System Technical Journal.

[2]  M. Schetzen,et al.  Nonlinear system modeling based on the Wiener theory , 1981, Proceedings of the IEEE.

[3]  P. J. Lawrence.  Estimation of the Volterra functional series of a nonlinear system using frequency-response data , 1981 .

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

[5]  S. Benedetto,et al.  Modeling and Performance Evaluation of Nonlinear Satellite Links-A Volterra Series Approach , 1979, IEEE Transactions on Aerospace and Electronic Systems.

[6]  Joe Brewer,et al.  Kronecker products and matrix calculus in system theory , 1978 .

[7]  Jiri Vlach,et al.  Distortion analysis of transistor networks , 1978 .

[8]  W. Rugh,et al.  Structural features of factorable Volterra systems , 1976 .

[9]  D. Weiner,et al.  A Scattering Variable Approach to the Volterra Analysis of Nonlinear Systems , 1976 .

[10]  Roger W. Brockett.  Volterra series and geometric control theory , 1976, Autom..

[11]  J. J. Bussgang,et al.  Analysis of nonlinear systems with multiple inputs , 1974 .

[12]  Joel Goldman.  A volterra series description of crosstalk interference in communications systems , 1973 .

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

[14]  S. Narayanan.  Application of Volterra series to intermodulation distortion analysis of transistor feedback amplifiers , 1970 .

[15]  S. Narayanan.  Intermodulation distortion of cascaded transistors , 1969 .

[16]  S. Narayanan,et al.  Noise Loading Analysis of a Third-Order Nonlinear System with Memory , 1968 .

[17]  S. Narayanan.  Transistor distortion analysis using volterra series representation , 1967 .

[18]  H. V. Trees.  Functional techniques for the analysis of the nonlinear behavior of phase–locked loops , 1964 .

[19]  Richard Bellman,et al.  Introduction to Matrix Analysis , 1972 .

[20]  D. A. George.  Continuous nonlinear systems , 1959 .