Abstract
In this paper, we investigate geometric properties of monotone systems by studying their isostables and basins of attraction. Isostables are boundaries of specific forward-invariant sets defined by the so-called Koopman operator, which provides a linear infinite-dimensional description of a nonlinear system. First, we study the spectral properties of the Koopman operator and the associated semigroup in the context of monotone systems. Our results generalize the celebrated Perron-Frobenius theorem to the nonlinear case and allow us to derive geometric properties of isostables and basins of attraction. Additionally, we show that under certain conditions we can characterize the bounds on the basins of attraction under parametric uncertainty in the vector field. We discuss computational approaches to estimate isostables and basins of attraction and illustrate the results on two and four state monotone systems.
| Original language | English |
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| Title of host publication | 2016 American Control Conference, ACC 2016 |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 7365-7370 |
| Number of pages | 6 |
| Volume | 2016-July |
| ISBN (Electronic) | 9781467386821 |
| DOIs | |
| Publication status | Published - 28 Jul 2016 |
| Externally published | Yes |
| Event | 2016 American Control Conference, ACC 2016 - Boston, United States Duration: 6 Jul 2016 → 8 Jul 2016 |
Conference
| Conference | 2016 American Control Conference, ACC 2016 |
|---|---|
| Country/Territory | United States |
| City | Boston |
| Period | 6/07/16 → 8/07/16 |
Keywords
- Basins of attraction
- Isostables
- Koopman operator
- Monotone systems
- Nonlinear Perron-Frobenius theorem