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2‐parameter root‐loci concepts and some applications
Author(s) -
Zeheb E.,
Walach E.
Publication year - 1977
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490050311
Subject(s) - root (linguistics) , root locus , rendering (computer graphics) , mathematics , locus (genetics) , complex plane , boundary (topology) , characteristic equation , stability (learning theory) , polynomial , mathematical analysis , computer science , differential equation , engineering , artificial intelligence , control system , philosophy , linguistics , biochemistry , chemistry , machine learning , electrical engineering , gene
Root‐locus concepts are expanded to treat characteristic expressions of systems and circuits with two parameters which vary along straight lines through the origin of the complex plane. Theorems are stated and proved by which the problem of finding the boundary of root regions of such expressions is reduced to the problem of plotting 1‐parameter root loci. The concepts of 2‐parameter root loci are then used to investigate the absolute stability of arbitrarily passively terminated 2‐ports. The following results are obtained by this method:1 The complete root regions of the characteristic equation are found, rendering more information about the dynamic behaviour of the 2‐ports than just determining absolute stability. 2 A new absolute stability criterion is proved which does not necessitate checking a polynomial for nonnegativeness along the imaginary axis. 3 A new proof of the Llewellyn criterion is arrived at.A numerical example is also provided for further clarification.