Separable Lyapunov functions for monotone systems
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 funct...
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Sprache: | eng |
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Zusammenfassung: | 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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ISSN: | 0191-2216 |
DOI: | 10.1109/CDC.2013.6760604 |