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arXiv · 2607.24595

Fixed-time stabilization of systems with nilpotent matrices in the presence of large unknown delays

Kang-Kang Zhang·Emilia Fridman·Pengfei Wang
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Abstract

In this paper, we study state-feedback fixed-time stabilization of continuous-time perturbed linear systems with nilpotent matrices in the presence of unknown large constant input/measurement delays with known bounds. By using an additional artificial delay, we design a feedback that for a precisely known linear system with a nilpotent matrix drives the state to zero in fixed time (which is larger than the bound of the unknown delay) and achieves input-to-state stability with a large exponential decay rate in the presence of additive disturbances and small system matrix perturbations and nonlinearities. For perturbed single integrators, fixed-time stabilization is achieved in the case of fast-varying unknown measurement delays with known bounds. The results are extended to discrete-time systems. Numerical simulations illustrate the efficiency of the results.

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Kang-Kang Zhang, Emilia Fridman, Pengfei Wang. 2026-08-21. Fixed-time stabilization of systems with nilpotent matrices in the presence of large unknown delays. https://arxiv.org/abs/2607.24595

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