期刊
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE
卷 47, 期 12, 页码 2965-2974出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207721.2015.1053830
关键词
harmonic; irreducibility; Floquet factorisation; controllability; reducibility
类别
资金
- National Science Foundation of China [61074186]
- Nature Science Foundation of Jiangsu Province, China [BK20140860]
The paper reports interesting but unnoticed facts about irreducibility (resp., reducibility) of Flouqet factorisations and their harmonic implication in term of controllability in finite-dimensional linear continuous-time periodic (FDLCP) systems. Reducibility and irreducibility are attributed to matrix logarithm algorithms during computing Floquet factorisations in FDLCP systems, which are a pair of essential features but remain unnoticed in the Floquet theory so far. The study reveals that reducible Floquet factorisations may bring in harmonic waves variance into the Fourier analysis of FDLCP systems that in turn may alter our interpretation of controllability when the Floquet factors are used separately during controllability testing; namely, controllability interpretation discrepancy (or simply, controllability discrepancy) may occur and must be examined whenever reducible Floquet factorisations are involved. On the contrary, when irreducible Floquet factorisations are employed, controllability interpretation discrepancy can be avoided. Examples are included to illustrate such observations.
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