Separable Lyapunov functions for monotone systems
A. Rantzer, B.S. Rüffer, G. Dirr, in: Proc. 52nd IEEE Conf. Decis. Control, 2013, pp. 4590–4594.
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Conference Paper
Author
Rantzer, Anders;
Rüffer, Björn S.;
Dirr, Gunther
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Abstract
Separable Lyapunov functions play vital roles, for example, in stability analysis of large-scale systems. A Lyapunov function is called max-separable if it can be decomposed into a maximum of functions with one-dimensional arguments. Similarly, it is called sum-separable if it is a sum of such functions. In this paper it is shown that for a monotone system on a compact state space, asymptotic stability implies existence of a max-separable Lyapunov function. We also construct two systems on a non-compact state space, for which a max-separable Lyapunov function does not exist. One of them has a sum-separable Lyapunov function. The other does not.
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Proceedings Title
Proc. 52nd IEEE Conf. Decis. Control
Page
4590–4594
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Cite this
Rantzer A, Rüffer BS, Dirr G. Separable Lyapunov functions for monotone systems. In: Proc. 52nd IEEE Conf. Decis. Control. ; 2013:4590–4594.
Rantzer, A., Rüffer, B. S., & Dirr, G. (2013). Separable Lyapunov functions for monotone systems. Proc. 52nd IEEE Conf. Decis. Control, 4590–4594.
@inproceedings{Rantzer_Rüffer_Dirr_2013, title={Separable Lyapunov functions for monotone systems}, booktitle={Proc. 52nd IEEE Conf. Decis. Control}, author={Rantzer, Anders and Rüffer, Björn S. and Dirr, Gunther}, year={2013}, pages={4590–4594} }
Rantzer, Anders, Björn S. Rüffer, and Gunther Dirr. “Separable Lyapunov Functions for Monotone Systems.” In Proc. 52nd IEEE Conf. Decis. Control, 4590–4594, 2013.
A. Rantzer, B. S. Rüffer, and G. Dirr, “Separable Lyapunov functions for monotone systems,” in Proc. 52nd IEEE Conf. Decis. Control, 2013, pp. 4590–4594.
Rantzer, Anders, et al. “Separable Lyapunov Functions for Monotone Systems.” Proc. 52nd IEEE Conf. Decis. Control, 2013, pp. 4590–4594.
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