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• W2406162175 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." @default.
• W2406162175 created "2016-06-24" @default.
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• W2406162175 creator A5019128476 @default.
• W2406162175 date "2015-10-05" @default.
• W2406162175 modified "2023-09-27" @default.
• W2406162175 title "Properties of Isostables and Basins of Attraction of Monotone Systems" @default.
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