Criteria for minimization of spectral abscissa of time-delay systems

doi:10.1007/s10483-021-2751-9

Applied Mathematics and Mechanics (English Edition) ›› 2021, Vol. 42 ›› Issue (7): 969-980.doi: https://doi.org/10.1007/s10483-021-2751-9

Criteria for minimization of spectral abscissa of time-delay systems

Zaihua WANG

Department of Basic Courses, Army Engineering University, Nanjing 211101, China

收稿日期:2020-12-07 修回日期:2021-04-28 发布日期:2021-06-24
通讯作者: Zaihua WANG, E-mail:zhwangnj@163.com
基金资助:
the National Natural Science Foundation of China (No. 12072370)

Criteria for minimization of spectral abscissa of time-delay systems

Zaihua WANG

Department of Basic Courses, Army Engineering University, Nanjing 211101, China

Received:2020-12-07 Revised:2021-04-28 Published:2021-06-24
Contact: Zaihua WANG, E-mail:zhwangnj@163.com
Supported by:
the National Natural Science Foundation of China (No. 12072370)

摘要/Abstract

摘要： 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.

关键词: time delay, stability, parameter tuning, spectral abscissa (SA), decaying speed

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.

Key words: time delay, stability, parameter tuning, spectral abscissa (SA), decaying speed

中图分类号:

34K20
93D15

Zaihua WANG. Criteria for minimization of spectral abscissa of time-delay systems[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(7): 969-980.

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Criteria for minimization of spectral abscissa of time-delay systems

Criteria for minimization of spectral abscissa of time-delay systems

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