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Titlebook: Bilinear Control Systems; Matrices in Action David Elliott Book 2009 Springer Science+Business Media B.V. 2009 Control Systems.Lie Algebras

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https://doi.org/10.1057/9781137301512This chapter, a supplement to Chapter 2, is a collection of standard definitions and basic facts drawn from Boothby [31], Conlon [64], Jacobson [143], Jurdjevic [147], and especially Varadarajan [282].
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Linearization,Often the phrase . . merely means the replacement of . by an approximating linear vector field. However, in this chapter it has a different meaning that began with the following question, important in the theory of dynamical systems, that was asked by Henri Poincaré [219]: . . on . . ., . . . . . . such that .?.
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Algebraic Geometry,The brief excursion here into algebraic geometry on affine spaces ., where . is . or ., is guided by the book of Cox et al. [67],which is a good source for basic facts about polynomial ideals, affine varieties, and symbolic algebraic computation.
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Applied Mathematical Scienceshttp://image.papertrans.cn/b/image/186232.jpg
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https://doi.org/10.1007/978-3-031-50914-8 differential equations ., where ., . is a square matrix, . is a locally integrable function and . ∈ . is a constant vector. The idea is that we have a dynamical system that left to itself would evolve on . as ., and a control term . can be added to influence the evolution. Linear control system the
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