Practical polynomial formulas in MIMO nonlinear realization problem

The explicit and simple polynomial formulas are given for computation of the (differentials) of state coordinates from the set of nonlinear input-output (i/o) equations under assumption that the set of i/o equations is realizable in the state-space form. The paper addresses a very wide class of nonlinear control systems, that accommodates continuous- as well as two discrete-time cases, based either on the shift or difference operator. Two types of polynomial formulas are suggested, based either on polynomial left division or on the application of the concept of adjoint polynomials and implemented in Mathematica-based software.