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´. Special forms are obtained for the transfer function, corresponding to the symmetric and triangular forms of the kernel. A new form is proposed for both the time-domain and transform-domain representation of homogeneous systems. 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.