Irreducibility Conditions for Continuous-time Multi-input Multi-output Nonlinear Systems

The purpose of this paper is to present necessary and sufficient condition for irreducibility of continuous-time nonlinear multi-input multi-output system. 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 basis 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