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.