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Canonical forms for stochastic nonlinear systems. (English) Zbl 1004.93005

An invariance-under-transformation rule is presented which associates any stochastic nonlinear system with a deterministic one in such a way that the association remains intact under coordinate transformation of both systems. With this rule, necessary and sufficient conditions for the existence of diffeomorphisms leading to various canonical forms for stochastic systems can be studied using the existing theory for deterministic systems. Three particular canonical forms are given for which the coordinate-independent conditions as well as the desired coordinate transformations are the same for the stochastic and the deterministic uncertain system.

MSC:

93B10 Canonical structure
93E03 Stochastic systems in control theory (general)
93B17 Transformations
93C10 Nonlinear systems in control theory
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