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Irreducibility, reduction and transfer equivalence of nonlinear input-output equations on homogeneous time scales. (English) Zbl 1184.93025
Summary: The purpose of this paper is to present a necessary and sufficient condition for irreducibility of nonlinear input-output delta differential equations. The condition is presented in terms of the common left divisor of two differential polynomials describing the behaviour of the system defined on a homogeneous time scale. The concept of reduction is explained. Subsequently, the definition of transfer equivalence based upon the notion of an irreducible differential form of the system is introduced, inspired by the analogous definition for continuous-time systems.

MSC:
93B11 System structure simplification
93B17 Transformations
93C10 Nonlinear systems in control theory
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