Irreducibility and reduction of nonlinear control systems: Unification and extension via pseudo-linear algebra

The paper applies the pseudo-linear algebra to unify the study of irreducibility and reduction for continuous-and discrete-time nonlinear control systems. The necessary and sufficient condition for irreducibility of nonlinear input-output equation is presented in terms of the common left factor of two polynomials describing the behaviour of the system. Besides unification, the tools of pseudo-linear algebra allow to extend the results for systems defined by difference, q-shift and q-difference operators.