On hybrid dynamical systems of differential–difference equations

• Published in: Chaos, solitons and fractals Vol. 187; p. 115431
• Main Authors: Dassios, Ioannis, Vaca, Angel, Milano, Federico
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2024
• Subjects: Differential–difference equations; Hybrid dynamical systems; Power systems stability; Stability analysis; Transfer function matrix; Hybrid dynamical systems; Differential–difference equations; Power systems stability; Stability analysis; Transfer function matrix
• ISSN: 0960-0779
• DOI: 10.1016/j.chaos.2024.115431

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.