Volume 48, Issue 12 pp. 12174-12185
RESEARCH ARTICLE

Resilient Control Strategies for Probabilistic Nonlinear Systems With Time Delays Subject to Scaling Attacks

Maya Joby

Corresponding Author

Maya Joby

SCMS Cochin School of Business, Kochi, Kerala, India

Correspondence:

Maya Joby ([email protected])

Contribution: Methodology, Conceptualization, Software, Validation, ​Investigation, Formal analysis, Visualization, Writing - review & editing, Writing - original draft

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M. Sathishkumar

M. Sathishkumar

Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu, India

Contribution: Methodology, Formal analysis, Visualization, Writing - original draft

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L. Susana Ramya

L. Susana Ramya

Department of Mathematics, KGiSL Institute of Technology, Coimbatore, India

Contribution: Conceptualization, Methodology, Validation, Visualization, Writing - original draft

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Srimanta Santra

Srimanta Santra

Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

Contribution: Conceptualization, Methodology, Supervision, Visualization, Validation, Writing - review & editing

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First published: 12 May 2025

Funding: The authors received no specific funding for this work.

ABSTRACT

This paper presents an observer-based control strategy for time-delay systems, where the time delay is considered to be variable to better reflect real-world applications. The system is further subjected to randomly varying input nonlinearity and scaling attacks. The input nonlinearity, exhibiting stochastic behavior, is modeled using a probabilistic framework with uncertain probabilities. To effectively characterize scaling attacks, a comprehensive model is introduced. The primary objective of this study is to establish tractable stability conditions with reduced conservatism. Using the Lyapunov–Krasovskii approach, a robust observer-based control strategy is developed, ensuring stability of the system. To further refine the stability conditions, delay fractionizing and matrix inequality techniques are employed, making the results dependent on the delay fraction size. By integrating these techniques, the proposed approach offers a systematic solution to the challenges associated with time-delay systems featuring variable delays and random input nonlinearity. Finally, numerical examples are provided to validate the effectiveness of the proposed control strategy, demonstrating its ability to achieve the desired system performance under the given conditions.

Conflicts of Interest

The authors declare no conflicts of interest.

Data Availability Statement

All data are provided in full in the results section of this paper.

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