abstract

• This paper presents a guided tour of some specific problems encountered in the stability analysis of linear dynamical systems including delays in their systems%27 representation. More precisely, we will address the characterization of multiple roots of the corresponding characteristic function with a particular emphasis on the way these roots are affected by the system%27s parameters and the way that they can be used to control. The paper covers several approaches (perturbation techniques, hypergeometric functions) leading to some methods and criteria (frequency-sweeping, multiplicity-induced-dominancy) that can be implemented (software toolboxes) for analyzing the qualitative and quantitative properties induced by the delays and other parameters on the system%27s dynamics. A particular attention will be paid to the so-called partial pole placement method based on the multiplicity-induced-dominancy property. The presentation is as simple as possible, focusing more on the main intuitive ideas and appropriate mathematical reasoning by analogy in the presentation of the theoretical results as well as their potential use in practical applications. Illustrative examples complete the paper. Copyright © 2021 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)
• This paper presents a guided tour of some specific problems encountered in the stability analysis of linear dynamical systems including delays in their systems' representation. More precisely, we will address the characterization of multiple roots of the corresponding characteristic function with a particular emphasis on the way these roots are affected by the system's parameters and the way that they can be used to control. The paper covers several approaches (perturbation techniques, hypergeometric functions) leading to some methods and criteria (frequency-sweeping, multiplicity-induced-dominancy) that can be implemented (software toolboxes) for analyzing the qualitative and quantitative properties induced by the delays and other parameters on the system's dynamics. A particular attention will be paid to the so-called partial pole placement method based on the multiplicity-induced-dominancy property. The presentation is as simple as possible, focusing more on the main intuitive ideas and appropriate mathematical reasoning by analogy in the presentation of the theoretical results as well as their potential use in practical applications. Illustrative examples complete the paper. Copyright © 2021 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)

authors

• Boussaada I.
• Méndez Barrios Cesar Fernando Francisco
• Niculescu S.-I.

publication date

• 2021-01-01

published in

• IFAC-PapersOnLine  Journal

keywords

• Asymptotic behavior; Delay; Dynamical systems; Frequency-sweeping; Multiplicity-induced-dominancy; Parameter-based methods; Weierstrass polynomial Linear control systems; Perturbation techniques; System stability; Asymptotic behaviour; Characteristic roots; Delay; Delay characteristics; Frequency sweeping; Multiple characteristics; Multiplicity-induced-dominancy; Parameter-based method; Property; Weierstrass polynomial; Dynamical systems

Digital Object Identifier (DOI)

• 10.1016/j.ifacol.2021.11.143

PubMed ID

start page

• 222

end page

• 239

volume

• 54

issue

• 18