New fixed-time synchronization results for discontinuous dynamic networks: A novel two-stage analysis approach

Shuiming Cai, Shulan Zhuang (), Jinyao Shi () and Peipei Zhou ()
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Shuiming Cai: School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, P. R. China
Shulan Zhuang: School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, P. R. China
Jinyao Shi: School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, P. R. China
Peipei Zhou: School of Mathematical Sciences, Jiangsu University, Zhenjiang 212013, P. R. China

International Journal of Modern Physics C (IJMPC), 2023, vol. 34, issue 11, 1-30

Abstract: This paper concerns the issue of fixed-time synchronization (FXTS) for complex networks composed of dynamical nodes with discontinuous dynamics, abbreviated as discontinuous dynamic networks, under the concept of Filippov solution. In terms of 1-norm and 2-norm, two types of simple control schemes without the linear feedback part are, respectively, designed to compel the considered discontinuous dynamic network to fixed-timely synchronize with a desired trajectory. By utilizing a novel two-stage analysis approach, some new FXTS criteria are derived. Compared with the existing research works, the established theoretical results not only are more relaxed, but also improve the estimation accuracy of synchronous settling time. Finally, the validity of the analytical results is verified via numerical simulations.

Keywords: Discontinuous dynamical networks; fixed-time synchronization; Filippov solution; two-stage analysis approach (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0129183123501486

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