Bilinear Control Systems: Matrices in Action
Bilinear Control Systems: Matrices in Action
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DOI：
10.5860/choice.47-1477
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发表时间：
2009-05
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影响因子：
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通讯作者：
D. Elliott
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文献类型：
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作者：
D. Elliott
一个控制系统被称为双线性的，如果它是由线性微分方程，其中的控制输入出现的系数。双线性控制系统的研究始于20世纪60年代，并已发展成为一个迷人的领域，对于解决许多具有挑战性的实际控制问题至关重要。它的方法和应用跨越了学科间的界限，在量子物理学中的自旋控制和李群研究等不同领域都很有用。这本书的前半部分是基于矩阵分析，介绍李代数和坎贝尔贝克豪斯多夫定理。个别章节致力于主题，如离散时间系统，可观测性和实现，从科学和工程的例子，非线性系统的线性化，和输入输出分析。由该领域的领先研究人员之一以清晰和可理解的方式编写，并配有证明，练习和Mathematica脚本，这涉及文本将是控制理论一年级研究生对该主题的重要和全面介绍。它也将是非常有价值的学者和研究人员与矩阵分析，李代数和半群的兴趣。
A control system is called bilinear if it is described by linear differential equations in which the control inputs appear as coefficients. The study of bilinear control systems began in the 1960s and has since developed into a fascinating field, vital for the solution of many challenging practical control problems. Its methods and applications cross inter-disciplinary boundaries, proving useful in areas as diverse as spin control in quantum physics and the study of Lie semigroups. The first half of the book is based upon matrix analysis, introducing Lie algebras and the Campbell-Baker-Hausdorff Theorem. Individual chapters are dedicated to topics such as discrete-time systems, observability and realization, examples from science and engineering, linearization of nonlinear systems, and input-output analysis. Written by one of the leading researchers in the field in a clear and comprehensible manner and laden with proofs, exercises and Mathematica scripts, this involving text will be a vital and thorough introduction to the subject for first-year graduate students of control theory. It will also be of great value to academics and researchers with an interest in matrix analysis, Lie algebra, and semigroups.