Abstract
Spectral abscissa (SA) is defined as the real part of the rightmost characteristic root(s) of a dynamical system, and it can be regarded as the decaying rate of the system, the smaller the better from the viewpoint of fast stabilization. Based on the Puiseux series expansion of complex-valued functions, this paper shows that the SA can be minimized within a given delay interval at values where the characteristic equation has repeated roots with multiplicity 2 or 3. Four sufficient conditions in terms of the partial derivatives of the characteristic function are established for testing whether the SA is minimized or not, and they can be tested directly and easily.
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26 July 2021
The author name was incorrectly mispelled during original upload. The author “Zaihua WANQ” should be “Zaihua WANG”.
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Citation: WANG, Z. H. Criteria for minimization of spectral abscissa of time-delay systems. Applied Mathematics and Mechanics (English Edition), 42(7), 969–980 (2021) https://doi.org/10.1007/s10483-021-2751-9
Project supported by the National Natural Science Foundation of China (No. 12072370)
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Wang, Z. Criteria for minimization of spectral abscissa of time-delay systems. Appl. Math. Mech.-Engl. Ed. 42, 969–980 (2021). https://doi.org/10.1007/s10483-021-2751-9
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DOI: https://doi.org/10.1007/s10483-021-2751-9