Non-fragile sampled-data control for synchronizing Markov jump Lur'e systems with time-variant delay

Dandan Zuo; Wansheng Wang; Lulu Zhang; Jing Han; Ling Chen; Dandan Zuo; Wansheng Wang; Lulu Zhang; Jing Han; Ling Chen

doi:10.3934/era.2024211

Electronic Research Archive

2024, Volume 32, Issue 7: 4632-4658. doi: 10.3934/era.2024211

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Research article

Non-fragile sampled-data control for synchronizing Markov jump Lur'e systems with time-variant delay

1.
School of Big Data & Artificial Intelligence, Ma'anshan University, Ma'anshan 243100, China
2.
School of Electrical and Information Engineering, Wanjiang University of Technology, Ma'anshan 243031, China

Received: 16 March 2024 Revised: 15 July 2024 Accepted: 23 July 2024 Published: 26 July 2024

The issue of non-fragile sampled-data control for synchronizing Markov jump Lur'e systems (MJLSs) with time-variant delay was investigated. The time-variant delay allowed for uncertainty that was constrained to an interval with defined upper and lower boundaries. The components of the nonlinear function within the MJLSs were considered to satisfy either Lipschitz continuity or non-decreasing monotonicity. Numerically tractable conditions that ensured stochastic synchronization with a predefined $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ disturbance attenuation level for the drive-response MJLSs were established, utilizing time-dependent two-sided loop Lyapunov-Krasovskii functionals, together with integral and matrix inequalities. An exact mathematical expression of the desired controller gains can be obtained based on these conditions. Finally, an example with numerical simulation was employed to demonstrate the effectiveness of the proposed control strategies.
- synchronization,
- Lur'e system,
- time delay,
- Markov jump process,
- sampled-data control,
- non-fragile control
Citation: Dandan Zuo, Wansheng Wang, Lulu Zhang, Jing Han, Ling Chen. Non-fragile sampled-data control for synchronizing Markov jump Lur'e systems with time-variant delay[J]. Electronic Research Archive, 2024, 32(7): 4632-4658. doi: 10.3934/era.2024211

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Abstract

The issue of non-fragile sampled-data control for synchronizing Markov jump Lur'e systems (MJLSs) with time-variant delay was investigated. The time-variant delay allowed for uncertainty that was constrained to an interval with defined upper and lower boundaries. The components of the nonlinear function within the MJLSs were considered to satisfy either Lipschitz continuity or non-decreasing monotonicity. Numerically tractable conditions that ensured stochastic synchronization with a predefined $ \mathcal{L}_{2}-\mathcal{L}_{\infty} $ disturbance attenuation level for the drive-response MJLSs were established, utilizing time-dependent two-sided loop Lyapunov-Krasovskii functionals, together with integral and matrix inequalities. An exact mathematical expression of the desired controller gains can be obtained based on these conditions. Finally, an example with numerical simulation was employed to demonstrate the effectiveness of the proposed control strategies.

References

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