Preassigned-time stability criteria for discontinuous nonautonomous systems: application to cluster synchronization in community networks

Zengyun Wang; Zuowei Cai; Aitong Xin; Yuxin Zhong; Zengyun Wang; Zuowei Cai; Aitong Xin; Yuxin Zhong

doi:10.3934/era.2026214

Electronic Research Archive

2026, Volume 34, Issue 7: 4846-4867. doi: 10.3934/era.2026214

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Research article

Preassigned-time stability criteria for discontinuous nonautonomous systems: application to cluster synchronization in community networks

1.
School of Mathematics and Statistics, Hunan First Normal University, Changsha 410205, China
2.
Hunan Provincial University Key Laboratory for Big Data Analysis and Application, Hunan First Normal University, Hunan 410205, China
3.
College of Information Science and Engineering, Hunan Women's University, Changsha 410002, China
4.
School of Computer Science, Hunan First Normal University, Changsha 410205, China

Received: 25 March 2026 Revised: 22 May 2026 Accepted: 28 May 2025 Published: 05 June 2026

This work investigated predefined-time stability for discontinuous nonautonomous systems and its application to cluster synchronization in community networks with discontinuous intra-community interactions. First, a new predefined-time stability criterion for nonautonomous systems was established via differential inclusions and a generalized Lyapunov method, allowing indefinite time derivatives almost everywhere. Second, a community network model was introduced incorporating discontinuous intra-community interactions, time-varying parameters, and sign-dependent coupling to represent cooperative and competitive relationships. For such networks, a state-feedback control protocol was designed that, using the proposed stability result, ensures cluster synchronization within any prescribed time. A numerical example with sign-based coupling validated the theoretical analysis.
Citation: Zengyun Wang, Zuowei Cai, Aitong Xin, Yuxin Zhong. Preassigned-time stability criteria for discontinuous nonautonomous systems: application to cluster synchronization in community networks[J]. Electronic Research Archive, 2026, 34(7): 4846-4867. doi: 10.3934/era.2026214

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Abstract

This work investigated predefined-time stability for discontinuous nonautonomous systems and its application to cluster synchronization in community networks with discontinuous intra-community interactions. First, a new predefined-time stability criterion for nonautonomous systems was established via differential inclusions and a generalized Lyapunov method, allowing indefinite time derivatives almost everywhere. Second, a community network model was introduced incorporating discontinuous intra-community interactions, time-varying parameters, and sign-dependent coupling to represent cooperative and competitive relationships. For such networks, a state-feedback control protocol was designed that, using the proposed stability result, ensures cluster synchronization within any prescribed time. A numerical example with sign-based coupling validated the theoretical analysis.

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