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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2302.05604 |
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Table of Contents:
- This paper considers the robustness of an uncertain nonlinear system along a finite-horizon trajectory. The uncertain system is modeled as a connection of a nonlinear system and a perturbation. The analysis relies on three ingredients. First, the nonlinear system is approximated by a linear time-varying (LTV) system via linearization along a trajectory. This linearization introduces an additional forcing input due to the nominal trajectory. Second, the input/output behavior of the perturbation is described by time-domain, integral quadratic constraints (IQCs). Third, a dissipation inequality is formulated to bound the worst-case deviation of an output signal due to the uncertainty. These steps yield a differential linear matrix inequality (DLMI) condition to bound the worst-case performance. The robustness condition is then converted to an equivalent condition in terms of a Riccati Differential Equation. This yields a computational method that avoids heuristics often used to solve DLMIs, e.g. time gridding. The approach is demonstrated by a two-link robotic arm example.