On hybrid dynamical systems of differential–difference equations
In this paper, we define and study a class of linear hybrid dynamical systems characterized by differential–difference equations. We introduce two operators that facilitate the analysis of these systems and derive explicit formulas for their solutions. We examine the transfer function matrix and cha...
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| Published in | Chaos, solitons and fractals Vol. 187; p. 115431 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.10.2024
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0960-0779 |
| DOI | 10.1016/j.chaos.2024.115431 |
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| Abstract | In this paper, we define and study a class of linear hybrid dynamical systems characterized by differential–difference equations. We introduce two operators that facilitate the analysis of these systems and derive explicit formulas for their solutions. We examine the transfer function matrix and characteristic polynomial to assess stability. Our theoretical findings are supported by numerical examples, demonstrating their application in power systems stability analysis. Specifically, we substantiate our theory within the context of power systems stability analysis, incorporating elements of discrete behavior.
•We study linear hybrid dynamical systems of differential–difference equations.•We define two operators to study solutions of the proposed hybrid systems.•We analyze the transfer function matrix, characteristic polynomial, and system stability.•We apply our theory to power systems stability with discrete behavior elements. |
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| AbstractList | In this paper, we define and study a class of linear hybrid dynamical systems characterized by differential–difference equations. We introduce two operators that facilitate the analysis of these systems and derive explicit formulas for their solutions. We examine the transfer function matrix and characteristic polynomial to assess stability. Our theoretical findings are supported by numerical examples, demonstrating their application in power systems stability analysis. Specifically, we substantiate our theory within the context of power systems stability analysis, incorporating elements of discrete behavior.
•We study linear hybrid dynamical systems of differential–difference equations.•We define two operators to study solutions of the proposed hybrid systems.•We analyze the transfer function matrix, characteristic polynomial, and system stability.•We apply our theory to power systems stability with discrete behavior elements. |
| ArticleNumber | 115431 |
| Author | Milano, Federico Vaca, Angel Dassios, Ioannis |
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| Cites_doi | 10.1109/TPWRS.2007.907349 10.1109/TPWRS.2005.856990 10.1007/BF01776566 10.1080/00207170410001726796 10.1108/03684920910976835 10.3390/math11061338 10.1007/s00034-012-9400-7 10.1109/TPWRS.2021.3061584 10.1109/TPWRS.2019.2940416 10.1007/s10703-013-0196-2 |
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| Keywords | Hybrid dynamical systems Differential–difference equations Power systems stability Stability analysis Transfer function matrix |
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