Given a minimal realization realizing the impulse response of a number of input channels, and given the impulse response of an additional input channel, a method will be derived for obtaining a minimal realization realizing the impulse response of this larger set of input channels.
It will be shown that the originally given minimal realization may form part of the new obtained minimal realization. This construction will be the basis of the minimal realization algorithm derived in this paper. It will be shown that besides the determination of the rank of Hankel matrices the algorithm only requires the solving of linear equations.
Keywords: Multi-input systems, Minimal realization theory. Input channel recursive approach, Hermite canonical forms.