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Improved Stability and \(H_{\infty }\) Performance Criteria for Teleoperation Delay-Dependent Systems: SSG and Input–output Approaches

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Abstract

In this study, a stability analysis and \( H_{\infty } \) performance are derived for the bilateral teleoperation systems with time-varying delay. A new model transformation is firstly applied by employing a three-term approximation for the delayed state with the scaled small-gain theorem (SSG). By using appropriate Lyapunov–Krasovskii functional (LKF) and a generalized free-matrix-based integral inequality, new stability analysis and \( H_{\infty } \) performance criteria are proposed in terms of linear matrix inequalities. Finally, the engineering relevance of theory has been highlighted with different examples.

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Data Availability

The datasets generated during the current study are available from the corresponding author on reasonable request.

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Author information

Authors and Affiliations

  1. Engineering Systems and Applications Laboratory, Sidi Mohammed Ben Abdellah University, National School of Applied Sciences, BP 72, My Abdallah Avenue Km.5 Imouzzer Road, Fez, Morocco

    Amal Hader & Mohammed Alfidi

  2. Engineering Sciences Laboratory, Polydisciplinary Faculty, Sidi Mohammed Ben Abdellah University, BP 1223, Oujda Road, Taza, Morocco

    Chakir El-Kasri

  3. LESSI Laboratory, Faculty of Sciences Dhar El Mehraz, Sidi Mohammed Ben Abdellah University, BP 1796, Fez, Morocco

    Elhoussaine Tissir

Authors
  1. Amal Hader
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  2. Chakir El-Kasri
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  3. Elhoussaine Tissir
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  4. Mohammed Alfidi
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Correspondence to Amal Hader.

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Hader, A., El-Kasri, C., Tissir, E. et al. Improved Stability and \(H_{\infty }\) Performance Criteria for Teleoperation Delay-Dependent Systems: SSG and Input–output Approaches. Circuits Syst Signal Process 42, 5187–5206 (2023). https://doi.org/10.1007/s00034-023-02362-x

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  • DOI: https://doi.org/10.1007/s00034-023-02362-x

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