Input - Output Equivalence Transformations for Discrete - Time Nonlinear Systems

The paper characterizes the input-output (i/o) equivalence transformations for discrete-time nonlinear system described by the set of nonlinear higher order difference equations in the inputs and the outputs. It has been demonstrated that applying the i/o equivalence transformation to the set of equations ϕ = 0 amounts to multiplying ϕ from left by the unimodular matrix U (δ), whose entries are non-commutative polynomials in the forward-shift operator δ. Then it has been proved that using the i/o equivalence transformations, the set of equations can be transformed into the row-reduced form, whenever the set of equations is well-defined. Finally, the constructive algorithm is provided for calculation of the transformation, which extends the corresponding transformation for linear systems and is directly implementable via the computer algebra systems like Mathematica or Maple. Copyright c 2004 IFAC.