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arXiv · 2501.08688

Some remarks on practical stabilization via CLF-based control under measurement noise

Patrick Schmidt·Pavel Osinenko·Stefan Streif
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Abstract

Practical stabilization of input-affine systems in the presence of measurement errors and input constraints is considered in this brief note. Assuming that a Lyapunov function and a stabilizing control exist for an input-affine system, the required measurement accuracy at each point of the state space is computed. This is done via the Lyapunov function-based decay condition, which describes along with the input constraints a set of admissible controls. Afterwards, the measurement time points are computed based on the system dynamics. It is shown that between these self-triggered measurement time points, the system evolves and converges into the so-called target ball, i.e. a vicinity of the origin, where it remains. Furthermore, it is shown that the approach ensures the existence of a control law, which is admissible for all possible states and it introduces a connection between measurement time points, measurement accuracy, target ball, and decay. The results of the approach are shown in three examples.

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Patrick Schmidt, Pavel Osinenko, Stefan Streif. 2025-01-15. Some remarks on practical stabilization via CLF-based control under measurement noise. https://arxiv.org/abs/2501.08688

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