Abstract
AbstractThis paper considers the nondeterministic operator G defined on the direct product space of a completely matrizable linear space × and a metric space Y; G is introduced as a projective set G (x, y) ⊂ × for arbitrary × ϵ × and y ϵ Y. Relating to the completely continuous operator f(x) with Y as the range, a fixed‐point theorem is given for the generalized operator equation × ϵ G (x, f(x)). This mathematical theory is applied to the analysis of deviation of the output response when a nondeterministic fluctuation is imposed on the internal structure, internal parameter or input signal of a system. As a result, clear definitions are given for the tolerability and quasitolerability of the system fluctuation, the stability and quasistability of the system, and the tolerability and quasitolerability of the system model and simulation by it. An aspect of the system's sensitivity analysis is also discussed. Of particular importance in this paper is the new proposal of the new concepts of quasitolerability and quasistability, which suggests that these concepts should be utilized more widely the notions of the system and its model by developing the computing abilities.
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