Robust stability analysis of large-scale interconnected systems with time-varying delays

Xiaoyu Sun; Huabo Liu; Bin Wang; Xiaoyu Sun; Huabo Liu; Bin Wang

doi:10.3934/math.2025445

AIMS Mathematics

2025, Volume 10, Issue 4: 9674-9696. doi: 10.3934/math.2025445

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Research article

Robust stability analysis of large-scale interconnected systems with time-varying delays

1.
School of Automation, Qingdao University, Qingdao 266071, China
2.
Shandong Key Laboratory of Industrial Control Technology, Qingdao 266071, China
3.
Qingdao Radio and Television Station, Qingdao 266071, China

Received: 13 December 2024 Revised: 16 March 2025 Accepted: 11 April 2025 Published: 25 April 2025
MSC : 15A39, 93A15, 93D09

The robust stability analysis of large-scale interconnected systems constrained by time-varying delays among subsystems is studied. In practical engineering applications, due to the spatially distributed nature of large-scale interconnected systems, the transfer of information among subsystems is usually affected by communication delays. Based on the integral quadratic constraint theory, the calculationally efficient conditions of robust stability for the large-scale interconnected systems were established by taking advantage of the sparsity of the subsystem connection topology. The derived decoupling robust stability conditions rely solely on the subsystem connection matrix, each subsystem parameter and the chosen integral quadratic constraint multiplier. Finally, the simulation results showed that the obtained conditions are valid for the analysis of large-scale interconnected systems constrained by time-varying delays among subsystems.
- large-scale systems,
- interconnected systems,
- robust stability,
- integral quadratic constraint,
- time-varying delays
Citation: Xiaoyu Sun, Huabo Liu, Bin Wang. Robust stability analysis of large-scale interconnected systems with time-varying delays[J]. AIMS Mathematics, 2025, 10(4): 9674-9696. doi: 10.3934/math.2025445

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Abstract

The robust stability analysis of large-scale interconnected systems constrained by time-varying delays among subsystems is studied. In practical engineering applications, due to the spatially distributed nature of large-scale interconnected systems, the transfer of information among subsystems is usually affected by communication delays. Based on the integral quadratic constraint theory, the calculationally efficient conditions of robust stability for the large-scale interconnected systems were established by taking advantage of the sparsity of the subsystem connection topology. The derived decoupling robust stability conditions rely solely on the subsystem connection matrix, each subsystem parameter and the chosen integral quadratic constraint multiplier. Finally, the simulation results showed that the obtained conditions are valid for the analysis of large-scale interconnected systems constrained by time-varying delays among subsystems.

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