Robust memory control design for semi-Markovian jump systems with cyber attacks

Ramalingam Sakthivel; Palanisamy Selvaraj; Oh-Min Kwon; Seong-Gon Choi; Rathinasamy Sakthivel; Ramalingam Sakthivel; Palanisamy Selvaraj; Oh-Min Kwon; Seong-Gon Choi; Rathinasamy Sakthivel

doi:10.3934/era.2023378

Electronic Research Archive

2023, Volume 31, Issue 12: 7496-7510. doi: 10.3934/era.2023378

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Robust memory control design for semi-Markovian jump systems with cyber attacks

1.
School of Electrical Engineering, Chungbuk National University, Cheongju 28644, South Korea
2.
School of Information and Communication Engineering, Chungbuk National University, Cheongju 28644, South Korea
3.
Department of Applied Mathematics, Bharathiar University, Coimbatore 641046, India
4.
Department of Mathematics, Sungkyunkwan University, Suwon 440746, South Korea

Received: 08 September 2023 Revised: 02 November 2023 Accepted: 16 November 2023 Published: 24 November 2023

This paper addressed the problem of observer-based memory state feedback control design for semi-Markovian jump systems subject to input delays and external disturbances, where the measurement output was vulnerable to randomly occurring cyber attacks. To facilitate analysis, the cyber attacks were described by a nonlinear function that meets Lipschitz continuity and the possible attack scenarios were represented by a stochastic parameter that follows the Bernoulli distribution. Based on the information from the considered system and state observer, an augmented closed loop system was constructed. Then, by using the Lyapunov stability theory, an extended Wirtinger's integral inequality and stochastic analysis, the required stability criterion was proposed in the form of linear matrix inequalities. As a result, the control and observer gain matrices were efficiently derived, ensuring the stochastic stability of closed-loop systems with $ H_\infty $ performance, regardless of cyber attacks. To demonstrate the effectiveness and theoretical value of the proposed robust memory state feedback control design, simulation results were presented.
- memory control,
- semi-Markovian jump systems,
- input delays,
- cyber attacks
Citation: Ramalingam Sakthivel, Palanisamy Selvaraj, Oh-Min Kwon, Seong-Gon Choi, Rathinasamy Sakthivel. Robust memory control design for semi-Markovian jump systems with cyber attacks[J]. Electronic Research Archive, 2023, 31(12): 7496-7510. doi: 10.3934/era.2023378

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Abstract

This paper addressed the problem of observer-based memory state feedback control design for semi-Markovian jump systems subject to input delays and external disturbances, where the measurement output was vulnerable to randomly occurring cyber attacks. To facilitate analysis, the cyber attacks were described by a nonlinear function that meets Lipschitz continuity and the possible attack scenarios were represented by a stochastic parameter that follows the Bernoulli distribution. Based on the information from the considered system and state observer, an augmented closed loop system was constructed. Then, by using the Lyapunov stability theory, an extended Wirtinger's integral inequality and stochastic analysis, the required stability criterion was proposed in the form of linear matrix inequalities. As a result, the control and observer gain matrices were efficiently derived, ensuring the stochastic stability of closed-loop systems with $ H_\infty $ performance, regardless of cyber attacks. To demonstrate the effectiveness and theoretical value of the proposed robust memory state feedback control design, simulation results were presented.

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