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Robust Disturbance Attenuation with Stability for Discrete-Time Singularly Perturbed Systems with Nonlinear Disturbances.

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Title: Robust Disturbance Attenuation with Stability for Discrete-Time Singularly Perturbed Systems with Nonlinear Disturbances.
Authors: Liu, Wei1,2 (AUTHOR) liuweiecnu@163.com, Wang, Yanyan1 (AUTHOR) yywang918@163.com, Wang, Zhiming2 (AUTHOR) zmwang@math.ecnu.edu.cn
Source: Circuits, Systems & Signal Processing. Aug2025, Vol. 44 Issue 8, p5693-5714. 22p.
Subjects: Linear control systems, Linear matrix inequalities, Discrete-time systems, Closed loop systems, Nonlinear systems
Abstract: The robust disturbance attenuation problem for a class of weak nonlinear discrete-time singularly perturbed systems is addressed. By using the fixed-point principle, we first find a sufficient condition to guarantee that the given system is standard. In this case, the original system is decomposed into the continuous-time slow subsystem and discrete-time fast subsystem, respectively. Then, based on the established results for the corresponding slow and fast subsystems, it is shown that the original system is asymptotically stable with a prescribed H∞ norm bound for sufficiently small values of the perturbation parameter, and the H∞ performance is still preserved as ε → 0 . For the case where the nominal system is unstable or the desired H∞ performance cannot be achieved, the problem of designing a control law to make the resulting closed-loop system asymptotically stable with a prescribed H∞ performance is further addressed. Finally, two numerical examples are given to show the effectiveness of the developed theoretical results. [ABSTRACT FROM AUTHOR]
Copyright of Circuits, Systems & Signal Processing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Robust Disturbance Attenuation with Stability for Discrete-Time Singularly Perturbed Systems with Nonlinear Disturbances.
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  Data: The robust disturbance attenuation problem for a class of weak nonlinear discrete-time singularly perturbed systems is addressed. By using the fixed-point principle, we first find a sufficient condition to guarantee that the given system is standard. In this case, the original system is decomposed into the continuous-time slow subsystem and discrete-time fast subsystem, respectively. Then, based on the established results for the corresponding slow and fast subsystems, it is shown that the original system is asymptotically stable with a prescribed H∞ norm bound for sufficiently small values of the perturbation parameter, and the H∞ performance is still preserved as ε → 0 . For the case where the nominal system is unstable or the desired H∞ performance cannot be achieved, the problem of designing a control law to make the resulting closed-loop system asymptotically stable with a prescribed H∞ performance is further addressed. Finally, two numerical examples are given to show the effectiveness of the developed theoretical results. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Circuits, Systems & Signal Processing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Text: English
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        Type: general
      – SubjectFull: Linear matrix inequalities
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      – SubjectFull: Discrete-time systems
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      – SubjectFull: Closed loop systems
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      – TitleFull: Robust Disturbance Attenuation with Stability for Discrete-Time Singularly Perturbed Systems with Nonlinear Disturbances.
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              Text: Aug2025
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