Stability analysis and security control of nonlinear singular semi-Markov jump systems

Yang Song; Beiyan Yang; Jimin Wang; Yang Song; Beiyan Yang; Jimin Wang

doi:10.3934/era.2025001

Electronic Research Archive

2025, Volume 33, Issue 1: 1-25. doi: 10.3934/era.2025001

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Research article

Stability analysis and security control of nonlinear singular semi-Markov jump systems

1.
School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China
2.
Key Laboratory of Knowledge Automation for Industrial Processes, Ministry of Education, Beijing 100083, China

Received: 05 November 2024 Revised: 27 November 2024 Accepted: 06 December 2024 Published: 02 January 2025

This paper mainly studied the stochastic stability and the design of state feedback controllers for nonlinear singular continuous semi-Markov jump systems under false data injection attacks. Based on the Lyapunov function and the implicit function theorem, a basic stochastic stability condition of the system was given to ensure that the nonlinear singular semi-Markov jump system under attack was regular, impulse-free, unique, and stochastically stable. On this basis, the stochastic admissible linear matrix inequality conditions of the system were obtained by using the singular value decomposition of the matrix and Schur's complement lemma. To design the state feedback controller, based on the upper and lower bounds of the time-varying transition probability of the semi-Markov jump system and the singular value decomposition method, the stochastic stable linear matrix inequality condition of the closed-loop system under the false data injection attack was established. Finally, the validity and feasibility of the results were verified by numerical examples.
- semi-Markov jump systems,
- singular system,
- false data injection attacks,
- state feedback controller
Citation: Yang Song, Beiyan Yang, Jimin Wang. Stability analysis and security control of nonlinear singular semi-Markov jump systems[J]. Electronic Research Archive, 2025, 33(1): 1-25. doi: 10.3934/era.2025001

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Abstract

This paper mainly studied the stochastic stability and the design of state feedback controllers for nonlinear singular continuous semi-Markov jump systems under false data injection attacks. Based on the Lyapunov function and the implicit function theorem, a basic stochastic stability condition of the system was given to ensure that the nonlinear singular semi-Markov jump system under attack was regular, impulse-free, unique, and stochastically stable. On this basis, the stochastic admissible linear matrix inequality conditions of the system were obtained by using the singular value decomposition of the matrix and Schur's complement lemma. To design the state feedback controller, based on the upper and lower bounds of the time-varying transition probability of the semi-Markov jump system and the singular value decomposition method, the stochastic stable linear matrix inequality condition of the closed-loop system under the false data injection attack was established. Finally, the validity and feasibility of the results were verified by numerical examples.

References

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