## An algebraic framework generalizing the concept of transfer functions to nonlinear systems.(English)Zbl 1283.93077

Summary: An algebraic point of view in nonlinear control systems, built up by introducing a differential field of meromorphic functions and a vector space of differential forms, is in this paper extended by introducing skew polynomials. Such polynomials act as operators over a vector space of differential forms. The left skew polynomial ring defined over the field of meromorphic functions is embedded to its quotient field to provide a basis for a symbolic computation of nonlinear systems. Members of such a quotient field are suggested as the transfer functions of nonlinear systems whereby the concept of the transfer functions is generalized to nonlinear systems. The theory is applied to nonlinear control systems and argues the invariance of introduced transfer functions of nonlinear systems to static state transformations, the existence of input–output descriptions for state space representations, availability of transfer function algebra for nonlinear systems, etc.

### MSC:

 93B25 Algebraic methods 93C10 Nonlinear systems in control theory

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### References:

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