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arXiv · 2511.12567

On hyperexponential stabilization of a chain of integrators in continuous and discrete time subject to unmatched perturbations

Moussa Labbadi·Denis Efimov
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Abstract

A recursive time-varying state feedback is presented for a chain of integrators with unmatched perturbations in continuous and discrete time. In continuous time, it is shown that hyperexponential convergence is achieved for the first state variable \(x_1\), while the second state \(x_2\) remains bounded. For the other states, we establish ISS {\cb property} by saturating the growing {\cb control} gain. In discrete time, we use implicit Euler discretization to {\cb preserve} hyperexponential convergence. The main results are demonstrated through several examples of the proposed control laws, illustrating the conditions established for both continuous and discrete-time systems.

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Moussa Labbadi, Denis Efimov. 2025-11-16. On hyperexponential stabilization of a chain of integrators in continuous and discrete time subject to unmatched perturbations. https://arxiv.org/abs/2511.12567

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