Extension of the transfer function approach to the realization problem of nonlinear systems to discrete-time case

In this paper the polynomial approach to the realization problem of nonlinear control systems, i.e. the problem of finding an observable state space representation of a SISO nonlinear system described by an input-output equation, is extended to the discrete-time case. To find the solution the so-called adjoint polynomials and adjoint transfer functions are employed establishing direct connection to the solution known from linear systems. In addition, in case a system is not realizable it is shown that, unlike in continuous-time case, there always exists a postcompensator which, when combined with the system in series connection, makes compensated system realizable. Due to the possibility to use the transfer function algebra when combining systems this problem can be solved in natural way.