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- W4319067584 abstract "The system Φ:Bn×Bm→Bn is called p-combinational, p⩾1, if it has a state space decomposition Ψ1,Ψ2,...,Ψp of 1-combinational systems. This decomposition is proved to be unique, and Ψ1,Ψ2,...,Ψp are called the levels of Φ. These concepts are introduced, together with some examples, in the first three sections.Like in the case of the 1-combinational systems, if Φ is p-combinational then an input-output function χΦ:Bm→Bn may be defined. Function χΦ characterizes the stability of these systems, and this is shown in Section 36.4.The hazards of the p-combinational systems, p⩾2, represent the situations when the convergence ϕα(μ,u,k)→limk→∞ϕα(μ,u,k) under constant input (indicating stability) is not coordinate-wise monotonic, and they are mentioned in Section 36.5.In Section 36.6 we prove that the Cartesian product of combinational systems is combinational.We characterize in Section 36.7 the predecessors and successors of the points μ∈Bn, when Φ is p-combinational.We do not know exactly which is the relation between the isomorphisms and the p-combinational systems and we stated this problem, together with an example, in Sections 36.8, 36.9.An invariance property of O+(μ,u) when Φ is p-combinational and u is constant is given in Section 36.10.The basins of attraction and the attractors of the combinational systems are addressed in Section 36.11.The subsystems of the combinational systems are the topic of Section 36.12.In Section 36.13, we show the manner that the fundamental operating mode works in the case of the combinational systems, due to their stability." @default.
- W4319067584 created "2023-02-04" @default.
- W4319067584 date "2023-03-01" @default.
- W4319067584 modified "2023-10-18" @default.
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- W4319067584 doi "https://doi.org/10.1016/s0193-953x(23)00005-9" @default.
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