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

Jie Chen (1) , Silviu-Iulian Niculescu (2) , Peilin Fu (1)

1 UC Riverside - University of California [Riverside]
2 L2S - Laboratoire des signaux et systèmes

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.

Mots clés: frequency-sweeping tests; robust stability; time-delay systems; uncertain quasi-polynomials; vertex tests

Domaines: Automatique

Jie Chen, Silviu-Iulian Niculescu, Peilin Fu. Robust stability of quasi-polynomials Frequency-sweeping conditions and vertex tests. IEEE Transactions on Automatic Control, 2008, 53 (5), pp.1219-1234. ⟨10.1109/TAC.2008.923686⟩. ⟨hal-02195961⟩