Stability of Lyapunov redesign trajectory tracking control with unbounded perturbations -- A tube-based stability analysis
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909963284119552 |
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| author | Tietze, Niclas Wulff, Kai Reger, Johann |
| author_facet | Tietze, Niclas Wulff, Kai Reger, Johann |
| contents | Considering a nonlinear system in Byrnes-Isidori form that is subject to unbounded perturbations, we apply Lyapunov redesign via feedback linearisation for trajectory tracking. Leveraging the ideas of tube-based geometric characterisation of the invariance properties of the closed loop, we generalise the classical stability criterion from the~literature from constant to nonconstant reference trajectories. The proposed analysis is tailored to the Lyapunov redesign and the tracking problem insofar as we incorporate the reference trajectory and the transient decrease of the tracking error enforced by the controller. In particular, we exploit that the Lyapunov function of the tracking error satisfies a differential inequality, thereby guaranteeing that the solution of the closed loop remains in a contracting tube along the reference trajectory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04247 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of Lyapunov redesign trajectory tracking control with unbounded perturbations -- A tube-based stability analysis Tietze, Niclas Wulff, Kai Reger, Johann Systems and Control Optimization and Control Considering a nonlinear system in Byrnes-Isidori form that is subject to unbounded perturbations, we apply Lyapunov redesign via feedback linearisation for trajectory tracking. Leveraging the ideas of tube-based geometric characterisation of the invariance properties of the closed loop, we generalise the classical stability criterion from the~literature from constant to nonconstant reference trajectories. The proposed analysis is tailored to the Lyapunov redesign and the tracking problem insofar as we incorporate the reference trajectory and the transient decrease of the tracking error enforced by the controller. In particular, we exploit that the Lyapunov function of the tracking error satisfies a differential inequality, thereby guaranteeing that the solution of the closed loop remains in a contracting tube along the reference trajectory. |
| title | Stability of Lyapunov redesign trajectory tracking control with unbounded perturbations -- A tube-based stability analysis |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2512.04247 |