@article{Wang2026, 
author = {Zengyun Wang and Zuowei Cai and Aitong Xin and Yuxin Zhong},
title = {Preassigned-time stability criteria for discontinuous nonautonomous systems: application to cluster synchronization in community networks},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {7},
pages = {4846-4867},
keywords = {preassigned-time stability, discontinuous nonautonomous systems, generalized Lyapunov approach, community networks, discontinuous intra-community interaction},
url = {https://www.sciopen.com/article/10.3934/era.2026214},
doi = {10.3934/era.2026214},
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.}
}