An SMC strategy for neutral-type systems with time-varying delays using improved integral inequality and practical applications

Saravanan Shanmugam; Vadivel Rajarathinam; K. Chaisena; Mohamed Rhaima; Nallappan Gunasekaran; Saravanan Shanmugam; Vadivel Rajarathinam; K. Chaisena; Mohamed Rhaima; Nallappan Gunasekaran

doi:10.3934/math.20251200

AIMS Mathematics

2025, Volume 10, Issue 11: 27290-27313. doi: 10.3934/math.20251200

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Research article

An SMC strategy for neutral-type systems with time-varying delays using improved integral inequality and practical applications

1.
Center for Computational Biology, Easwari Engineering College, Chennai 600089, Tamil Nadu, India
2.
Center for Research, SRM Institute of Science and Technology-Ramapuram, Chennai 600089, Tamil Nadu, India
3.
Department of Mathematics, Phuket Rajabhat University, Phuket 83000, Thailand
4.
Department of Statistics and Operations Research, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia
5.
Eastern Michigan Joint College of Engineering, Beibu Gulf University, Qinzhou 535011, China

Received: 21 July 2025 Revised: 30 October 2025 Accepted: 10 November 2025 Published: 24 November 2025
MSC : 34D23, 93C10, 93C43, 93D30

In this paper, we investigates the sliding mode control (SMC) strategy for neutral-type systems with distributed time-varying delay using novel improved integral inequality, which has significant applications in fields such as control systems, communication networks, and biological systems. A standard Lyapunov-Krasovskii functional is introduced, complemented by improved integral inequality techniques and two types of time-delay methods (neutral type and distributed). These methodologies enabled the derivation of sufficient conditions, formulated as linear matrix inequalities, that ensured the asymptotic stability of the system utilizing the SMC technique. The proposed approach reduced conservatism in stability criteria by investigating improved integral inequalities and delay-dependent techniques, offering more accurate and efficient stability conditions. Numerical examples are presented to validate the theoretical findings with the practical application of partial element equivalent circuit (PEEC), showcasing the effectiveness and superiority of the proposed methodology over existing results.
- time-varying delay,
- linear matrix inequality,
- Lyapunov-Krasovskii functional,
- sliding-mode control,
- improved integral inequality
Citation: Saravanan Shanmugam, Vadivel Rajarathinam, K. Chaisena, Mohamed Rhaima, Nallappan Gunasekaran. An SMC strategy for neutral-type systems with time-varying delays using improved integral inequality and practical applications[J]. AIMS Mathematics, 2025, 10(11): 27290-27313. doi: 10.3934/math.20251200

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Abstract

In this paper, we investigates the sliding mode control (SMC) strategy for neutral-type systems with distributed time-varying delay using novel improved integral inequality, which has significant applications in fields such as control systems, communication networks, and biological systems. A standard Lyapunov-Krasovskii functional is introduced, complemented by improved integral inequality techniques and two types of time-delay methods (neutral type and distributed). These methodologies enabled the derivation of sufficient conditions, formulated as linear matrix inequalities, that ensured the asymptotic stability of the system utilizing the SMC technique. The proposed approach reduced conservatism in stability criteria by investigating improved integral inequalities and delay-dependent techniques, offering more accurate and efficient stability conditions. Numerical examples are presented to validate the theoretical findings with the practical application of partial element equivalent circuit (PEEC), showcasing the effectiveness and superiority of the proposed methodology over existing results.

References

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