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Robust Stability of Quasi-Polynomials: Frequency-Sweeping Conditions and Vertex Tests

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3 Author(s)
Jie Chen ; Dept. of Electr. Eng., California Univ., Riverside, CA ; Niculescu, S.-I. ; Peilin Fu

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.

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Automatic Control, IEEE Transactions on  (Volume:53 ,  Issue: 5 )