Research on the ellipsoidal boundary of reachable sets of neutral systems with bounded disturbances and discrete time delays

Beibei Su; Liang Zhao; Liang Du; Qun Gu; Beibei Su; Liang Zhao; Liang Du; Qun Gu

doi:10.3934/math.2024804

AIMS Mathematics

2024, Volume 9, Issue 6: 16586-16604. doi: 10.3934/math.2024804

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Research article

Research on the ellipsoidal boundary of reachable sets of neutral systems with bounded disturbances and discrete time delays

1.
Wuxi Vocational College of Science and Technology, Jiangsu Wuxi, 214000, China
2.
College of Information Engineering, Yangzhou University, Yangzhou 225127, China

Received: 28 March 2024 Revised: 03 May 2024 Accepted: 07 May 2024 Published: 13 May 2024
MSC : 34K40, 37B25

This research focuses on the challenge of defining the ellipsoidal boundaries of the reachable set (RS) for neutral-type dynamical systems with time delays. A novel analytical approach is proposed, leveraging the development of new Lyapunov functions and matrix inequality techniques. These methods provide powerful tools for determining the ellipsoidal boundaries of the system's RS. A comparative analysis, supported by numerical examples, demonstrates that the approach outlined in this study can accurately identify smaller yet effective RS boundaries compared to existing literature. This precise boundary determination offers significant theoretical support for state estimation and control design in dynamical systems, thereby enhancing their effectiveness and reliability in real-world applications.
- time delays,
- reachable set,
- neutral-type systems,
- bounded disturbances,
- Lyapunov function,
- ellipsoid boundary
Citation: Beibei Su, Liang Zhao, Liang Du, Qun Gu. Research on the ellipsoidal boundary of reachable sets of neutral systems with bounded disturbances and discrete time delays[J]. AIMS Mathematics, 2024, 9(6): 16586-16604. doi: 10.3934/math.2024804

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Abstract

This research focuses on the challenge of defining the ellipsoidal boundaries of the reachable set (RS) for neutral-type dynamical systems with time delays. A novel analytical approach is proposed, leveraging the development of new Lyapunov functions and matrix inequality techniques. These methods provide powerful tools for determining the ellipsoidal boundaries of the system's RS. A comparative analysis, supported by numerical examples, demonstrates that the approach outlined in this study can accurately identify smaller yet effective RS boundaries compared to existing literature. This precise boundary determination offers significant theoretical support for state estimation and control design in dynamical systems, thereby enhancing their effectiveness and reliability in real-world applications.

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