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On the Practical h-stability of Nonlinear Systems of Differential Equations

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Abstract

In this paper, we present a new notion of stability for nonlinear systems of differential equations called practical h-stability. Necessary and sufficient conditions for practical h-stability are given using the Lyapunov theory. Our original results generalize well-known fundamental results: practical exponential stability, practical asymptotic stability, and practical stability for nonlinear time-varying systems. In addition, these results are used to study the practical h-stability of two important classes of nonlinear systems, namely perturbed and cascaded systems. The last part is devoted to the study of the problem of practical h-stabilization for certain classes of nonlinear systems.

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Authors and Affiliations

  1. University of Gafsa, Gafsa, Tunisia

    B. Ghanmi

  2. Faculty of Sciences of Gafsa, Department of Mathematics, Sidi Ahmed Zarroug 2112, Gafsa, Tunisia

    B. Ghanmi

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  1. B. Ghanmi
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Correspondence to B. Ghanmi.

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Ghanmi, B. On the Practical h-stability of Nonlinear Systems of Differential Equations. J Dyn Control Syst 25, 691–713 (2019). https://doi.org/10.1007/s10883-019-09454-5

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  • DOI: https://doi.org/10.1007/s10883-019-09454-5

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