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- W4319782134 abstract "The combinational systems are the systems without feedback. Of them, the combinational systems with one level, shortly called 1-combinational systems, are defined as systems Φ:Bn×Bm→Bn that do not depend on the state coordinates: χΦ:Bm→Bn exists, such that ∀μ∈Bn,∀ν∈Bm,χΦ(ν)=Φ(μ,ν). Then χΦ is called the input-output function of Φ. If the input is constant, ∀k∈N,u(k)=ν, the system behaves like an autonomous system with constant generator function. These systems are introduced in Section 35.1 and in Section 35.2 we give examples. An important property of the combinational systems is stability, in particular the states of the 1-combinational systems with a constant input ν converge coordinate-wise monotonically towards the final value χΦ(ν), as shown in Section 35.3. The Cartesian product of 1-combinational systems and the predecessors/successors of such systems are addressed in Sections 35.4 and 35.5. The isomorphisms (h,h′,h″)∈Iso(Φ,Ψ) bring, in certain circumstances, the 1-combinational system Φ in the 1-combinational system Ψ. This, together with the special case when the isomorphisms are translations, is treated in Sections 35.6 and 35.7. A property of invariance when Φ is 1-combinational is given in Section 35.8. In Section 35.9 we characterize the subsystems of a 1-combinational system." @default.
- W4319782134 created "2023-02-11" @default.
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- W4319782134 date "2023-01-01" @default.
- W4319782134 modified "2023-09-28" @default.
- W4319782134 title "Combinational systems with one level" @default.
- W4319782134 doi "https://doi.org/10.1016/b978-0-32-395422-8.00041-6" @default.
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