Explicit formulas for the state coordinates in nonlinear MIMO realization problem on homogeneous time scales

The problem of realization of nonlinear multi-input multi-output equations, defined on homogeneous time scale, in the state-space form is studied. The polynomial approach, based on non-commutative ring of skew polynomials, allows to replace the existing step-by-step algorithm based on certain sequences of differential one-forms by explicit formulas to compute the differentials of the state coordinates directly from system description. Implementation details of the developed theory in the Mathematica environment are presented.