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- W1904909698 abstract "One striking aspect of the class of linear systems is that the controls enter in a way which is independent of the state; that is they are homogeneous, w.r.t. the underlying vectorspace (additive Lie group) structure as far as the controls are concerned, and the autonomous term enjoys reminiscent but not identical “homogeneity properties”. Another class of systems which enjoys such properties is the class of systems on Lie groups and coset spaces (E.g. ġ=(A+σuiBi)g, $$underline{underline G} underline{underline L} _n$$ , A, Bi ∈ gl n) studied by Brockett, Jurdjevic-Sussmann, Hirschhorn and others. However, in the case the Lie group G is the additive group this class does not specify to the familiar class of linear systems (but to $$dot x = a + sum u_i b_i , a, b_i in underline{underline R} ^n$$ ). Yet the analysis of these two classes of control systems suggests certain “family” characteristics. In this paper I discuss several aspects of classes of systems, which in one-way or another — there are several different choices one can make — generalize both the familiar linear systems and the class on Lie groups mentioned above." @default.
- W1904909698 created "2016-06-24" @default.
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- W1904909698 date "2005-10-05" @default.
- W1904909698 modified "2023-09-27" @default.
- W1904909698 title "Control and filtering of a class of nonlinear but “homogeneous” systems" @default.
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- W1904909698 doi "https://doi.org/10.1007/bfb0006824" @default.
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