- Title
- Separable Lyapunov functions for monotone systems: constructions and limitations
- Creator
- Dirr, Gunther; Ito, Hiroshi; Rantzer, Anders; Rüffer, Björn S.
- Relation
- Discrete and Continuous Dynamical Systems - Series B (DCDS-B) Vol. 20, Issue 8, p. 2497-2526
- Publisher Link
- http://dx.doi.org/10.3934/dcdsb.2015.20.2497
- Publisher
- American Institute of Mathematical Sciences (AIMS Press)
- Resource Type
- journal article
- Date
- 2015
- Description
- For monotone systems evolving on the positive orthant of Rn+ two types of Lyapunov functions are considered: Sum- and max-separable Lyapunov functions. One can be written as a sum, the other as a maximum of functions of scalar arguments. Several constructive existence results for both types are given. Notably, one construction provides a max-separable Lyapunov function that is defined at least on an arbitrarily large compact set, based on little more than the knowledge about one trajectory. Another construction for a class of planar systems yields a global sum-separable Lyapunov function, provided the right hand side satisfies a small-gain type condition. A number of examples demonstrate these methods and shed light on the relation between the shape of sublevel sets and the right hand side of the system equation. Negative examples show that there are indeed globally asymptotically stable systems that do not admit either type of Lyapunov function.
- Subject
- monotone systems; separable Lyapunov functions; converse Lyapunov theorems; explicit formulas; ordinary differential equations
- Identifier
- http://hdl.handle.net/1959.13/1326006
- Identifier
- uon:25346
- Identifier
- ISSN:1531-3492
- Language
- eng
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