A reliable graphical criterion for TDS stability analysis

The paper considers the stability issue of linear systems with commensurate delays. This issue can be well characterised by the distribution of roots of system's characteristic equation. At first, distribution boundary of the roots (with positive real parts) is explicit given in a practical way...

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Bibliographic Details
Published in:International journal of systems science 2020-01, Vol.51 (2), p.381-388
Main Authors: Cai, Tiao Yang, Jin, Hui Long, Xie, Xiang Peng
Format: Article
Language:English
Subjects:
argument principle
Characteristic functions
Complex systems
Eigenvalues
Eigenvectors
graphical criterion
Linear systems
Polynomials
Stability analysis
Stability criteria
Time delay system
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Summary:The paper considers the stability issue of linear systems with commensurate delays. This issue can be well characterised by the distribution of roots of system's characteristic equation. At first, distribution boundary of the roots (with positive real parts) is explicit given in a practical way. Subsequently, a reliable graphical stability criterion for calculating the number of unstable roots is deduced, associating with auxiliary polynomial which plays an important role in the analysis of high order and complex systems. Moreover, a procedure for drawing the winding curve of characteristic function in finite path is proposed. At last, typical examples are given to illustrate that the result carried out is reliable and efficient.
ISSN:0020-7721
1464-5319
DOI:10.1080/00207721.2020.1716098