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Realizations in feedforward forms of nonlinear input‐output equations with time‐delays

The article studies possibilities to find realization of nonlinear retarded control system with constant commensurable delays, described by higher order input‐output equation, in a set of first‐order equations, which is in the so‐called feedforward form. Necessary and sufficient conditions are found for solvability of the problem when the realization is assumed to be strongly observable, that is, when the states of the feedforward form can be represented as functions of system output, input, their time‐derivatives and delays. Though the extension follows, in general, the polynomial approach of the delay‐free case, it is nontrivial. For instance, polynomial division is not, in general, possible for polynomials, defined over ring. Three examples illustrate the results.