On transfer function representations for homogeneous nonlinear systems

For stationary, homogeneous, nonlinear systems described via the Volterra functional representation, the Laplace transform of the system kernel is commonly used as a "transfer function." Corresponding to the symmetric and triangular forms of the kernel, special forms are obtained for the transfer function. We propose a new form for both the time-domain and transform-domain representation of homogeneous systerns. Properties of these so-called regular forms in relation to the other two forms and in regard to input/output computation, stability, and bilinear realization theory are discussed.