This paper will provide a study of the delay-independent stability of uncertain control systems, represented by a family of quasipolynomials with single time-delays. The uncertain systems that are considered here are delay differential systems whose parameters are known only by their lower and upper bounds. The results are given in the form of necessary and sufficient conditions along with the assumptions for the quasipolynomial families considered. The conditions are transformed into convenient forms, which provide analytical expressions that can be easily checked by commercially available computing tools. For uncertain systems represented by families of quasipolynomials, it is shown that the delay independent stability for the extreme values of parameters is not sufficient for the delay independent stability of the entire family. In addition, the family must satisfy some conditions for the interior values of each parameter within specially constructed frequency ranges. The implementation of the theorem that is suggested is demonstrated on an example system that includes a single degree of freedom system with an active vibration absorber, namely the Delayed Resonator.
Delay-independent Stability of Uncertain Control Systems
Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received February 2001; Revised December 2001. Associate Editor: J. Wickert.
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Tuzcu, I., and Ahmadian, M. (March 26, 2002). "Delay-independent Stability of Uncertain Control Systems ." ASME. J. Vib. Acoust. April 2002; 124(2): 277–283. https://doi.org/10.1115/1.1458015
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