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On the Logarithmic Stability Estimates of Non-autonomous Systems: Applications to Control Systems

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Abstract

This paper concerns the polynomial-logarithmic stability and stabilization of time-varying control systems. We present sufficient Lyapunov-like conditions guaranteeing this polynomial-logarithmic stability with applications to several linear and nonlinear control systems.

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No datasets were generated or analysed during the current study.

Notes

  1. If this second condition holds for all \(r>0\), then \(0\in {\mathbb {R}}^n\) is said to be globally P-L stable for \(\dot{x}=X(t,\,x).\)

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Acknowledgements

The authors would like to thank the anonymous reviewers for valuable suggestions to improve the paper.

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Authors and Affiliations

  1. Ecole Nationale d’Ingénieurs de Tunis, Université Tunis El-Manar, Tunis, Tunisia

    Chaker Jammazi

  2. Laboratoire d’Ingénierie Mathématique (LIM), Ecole Polytechnique de Tunisie, Université de Carthage, Carthage, Tunisia

    Chaker Jammazi & Ghada Bouamaied

  3. Laboratoire CRAN, Université de Lorraine, INRIA Nancy Grand Est, Nancy, France

    Mohamed Boutayeb

Authors
  1. Chaker Jammazi
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  2. Ghada Bouamaied
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  3. Mohamed Boutayeb
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Contributions

The first author presented the problem with the analysis of theoretical results and the illustration of the main results by examples from control theory (Examples 3, 4 and 5). The third author presented some criticisms of some proofs by improving their quality. His intervention is again based on reasonable hypotheses in the Examples 3 and 4; while the second author, is responsible for presenting some examples of control systems (Examples 1 and 2 and the last Example in Section 4.1) and participates in the bibliography and the writing of the article.

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Correspondence to Chaker Jammazi.

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Jammazi, C., Bouamaied, G. & Boutayeb, M. On the Logarithmic Stability Estimates of Non-autonomous Systems: Applications to Control Systems. Qual. Theory Dyn. Syst. 23, 186 (2024). https://doi.org/10.1007/s12346-024-01040-w

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