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A unified Lyapunov-like characterization for predefined time synchronization of nonlinear systems

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Abstract

In this paper, we present a new design for predefined time stable Lyapunov-like characterizations. Our approach combines several previously proposed Lyapunov characterizations and provides a unified idea for designing predefined time stable dynamic systems, based on which the framework of the predefined time sliding mode controller (PTSMC) is designed. First, we define \({ Class }-\mathcal {Z}\) functions and use them to design a unified form of Lyapunov-like characterization; moreover, we prove that it satisfies the predefined time stability by using the comparison principle. Second, a class of predefined time stable dynamic systems is developed based on this constructed function, and its predefined time stability properties are confirmed by Lyapunov theory. Finally, the dynamic system is used to construct a sliding mode controller, and a universal framework for PTSMCs is designed. By applying the above to chaos synchronization, numerical simulations demonstrate the universality and the feasibility of this unified control framework.

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Data will be available by request after the publication of this paper.

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The present research received no specific grant from any funding agency.

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Authors and Affiliations

  1. Mathematics and Physics School, University of Science and Technology Beijing, Beijing, 100083, China

    Mengjiao Zhang, Hongyan Zang & Zhudong Shi

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  1. Mengjiao Zhang
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  2. Hongyan Zang
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  3. Zhudong Shi
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Contributions

Mengjiao Zhang: (Conceptualization: Lead; Data curation: Lead; Formal analysis: Lead; Investigation: Lead; Methodology: Lead; Software: Lead; Writing - original draft: Lead; Writing - review & editing: Lead.) Hongyan Zang: (Conceptualization: Lead; Formal analysis: Lead; Funding acquisition: Lead; Investigation: Lead; Project administration: Lead; Resources: Lead; Supervision: Lead; Validation: Lead.) Zhudong Shi: (Investigation: Supporting; Methodology: Lead; Software: Supporting; Validation: Lead; Visualization: Lead; Writing - original draft: Supporting; Writing - review & editing: Supporting.)

Corresponding author

Correspondence to Hongyan Zang.

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Zhang, M., Zang, H. & Shi, Z. A unified Lyapunov-like characterization for predefined time synchronization of nonlinear systems. Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-09506-x

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