A Modification of the Coates Gain Formula for the Analysis of Linear Systems†
作者:
S. PARK CHAN,
B. H. BAPNA,
期刊:
International Journal of Control
(Taylor Available online 1967)
卷期:
Volume 5,
issue 5
页码: 483-495
ISSN:0020-7179
年代: 1967
DOI:10.1080/00207176708921779
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
In this paper, the Coates flow-graph gain formula is modified by the introduction of the loop-set and the two-loop-set, baaed on the concepts of the tree and the two-tree in network topology. The analogy is evident by observing that the two-treesTijof a given graphGcan be obtained by coalescing verticesiandjofGand thon removing the self-loops. In a similar manner, the two-loop-sets can be obtained from the flow graph by first modifying the graph and then obtaining the loop-sets of tho modified graph. Because of such modification, the derivation of tho gain formula is considerably simplified. Consequently, the evaluation of the terms in the formula becomes easier. Finally, a simple method of determining the number of terms in the formula is derived as a check against possible omission of terms due to carelessness.
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