Reduction and transfer equivalence of nonlinear control systems: unification and extension via pseudo-linear algebra

The paper applies the pseudo-linear algebra to unify the results on reducibility, reduction and transfer equivalence for continuousand discrete-time nonlinear control systems. The necessary and sufficient condition for reducibility of nonlinear input-output equation is presented in terms of the greatest common left factor of two polynomials describing the behaviour of the ‘tangent linearized system’ equation. The procedure is given to find the reduced (irreducible) system equation that is transfer equivalent to the original system equation. Besides unification, the tools of pseudo-linear algebra allow to extend the results also for systems defined in terms of difference, q-shift and q-difference operators.