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- W164413689 abstract "Abstract In this paper we study large classes of non-linear systems admitting a transfer function which completely describes their input-output behaviour. Many concepts which are widely believed to be particular to linear systems turn over to this class of “separable” systems. These are systems ∑ = (Q, A, B, F, G) in which the map F, G can be separated as F(q, a) = α(q) + β(a), G(q, a) = γ(q) + δ(a), where Q, A, B are groups, α,γ maps and β,δ homomorphisms. If we study separable systems with identical input- and output groups then it turns out that the parallel- (the series-) connections of systems correspond to the addition (the composition, respectively) of their transfer functions. Hence these systems form a near-ring (the “non-linear analogue of a ring”) w.r.t. to parallel- and series connections. Many system-theoretic questions can be studied in the framework of near-rings. In particular, we study feedbacks, reachability questions, invertibility with delay L and close with a discussion of the realization problem of separable systems." @default.
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- W164413689 date "1987-01-01" @default.
- W164413689 modified "2023-09-25" @default.
- W164413689 title "Near-Rings and Non-Linear Dynamical Systems" @default.
- W164413689 cites W2169559045 @default.
- W164413689 doi "https://doi.org/10.1016/s0304-0208(08)72304-1" @default.
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