Structural features of factorable Volterra systems

Several structural features are investigated for the class of systems
\Pi_{K}
composed of
K
linear dynamic subsystems connected in parallel with outputs multiplied (in the time domain). Concepts of reachability and observability of
\Pi_{K}
are introduced and characterized in terms of properties of the symmetric Volterra transfer function and associated transform, respectively. An algorithm for realization is provided and it is shown that complete identification of
\Pi_{K}
can be accomplished from steady-state response measurements for a finite number of two-tone sinusoidal inputs.