Abstract
The purpose of this paper is to present necessary and sufficient condition for irreducibility of discrete-time nonlinear multi-input multi-output system which extends directly the corresponding condition for the linear case. The condition is presented in terms of the greatest common left divisor of two polynomial matrices related to the input-output equations of the system. The basic difference is that unlike the linear case the elements of the polynomial matrices belong to a non-commutative polynomial ring. This condition provides a bases for finding the equivalent minimal irreducible representation of the i/o equations which is a suitable starting point for constructing an observable and accessible state space realization.
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