Robust stability of quasi-polynomials : Frequency-sweeping conditions and vertex tests

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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  • Jie Chen
  • Silviu-Iulian Niculescu
  • Peilin Fu


Original languageEnglish
Pages (from-to)1219-1234
Journal / PublicationIEEE Transactions on Automatic Control
Issue number5
Publication statusPublished - 2008
Externally publishedYes


In this paper, we study the robust stability of uncertain time-delay systems. We consider uncertain quasi-polynomials whose coefficients may vary in a certain prescribed range. Our goal is to derive necessary and sufficient conditions for such uncertain quasi-polynomials to maintain stability independent of delay parameters. Our primary contributions are frequency-sweeping conditions for interval, diamond, and spherical quasi-polynomial families, which can be readily checked, requiring only the computation of two simple frequency-dependent functions. Additionally, we also obtain vertex- and edge-type results in the spirit of the Kharitonov approach known in robust stability analysis, showing that the stability of interval and diamond quasi-polynomials can be ascertained by checking the stability of certain special vertex and/or edge members in those families. Both type of results provide necessary and sufficient conditions for the quasi-polynomial families to be robustly stable independent of delay. © 2008 IEEE.

Research Area(s)

  • Frequency-sweeping tests, Robust stability, Timedelay systems, Uncertain quasi-polynomials, Vertex tests