- Title
- A Left Eigenvector Producing a Smooth Lyapunov Function of ISS Networks
- Creator
- Ito, Hiroshi; Rüffer, Björn S.
- Relation
- 6th International Conference on Positive Systems, POSTA 2018. Proceedings of 6th International Conference on Positive Systems, POSTA 2018, Volume 480 (Hangzhou, China 25-27 August, 2018) p. 247-268
- Relation
- ARC.DP160102138 http://purl.org/au-research/grants/arc/DP160102138
- Publisher Link
- http://dx.doi.org/10.1007/978-3-030-04327-8_20
- Publisher
- Springer
- Resource Type
- conference paper
- Date
- 2019
- Description
- For a class of monotone nonlinear systems, it is shown that a continuously differentiable Lyapunov function can be constructed implicitly from a left eigenvector of vector fields. The left eigenvector which is a continuous function of state variables is deduced from a right eigenvector which represents a small gain condition. It is demonstrated that rounding off the edges of n-orthotopes, which is the maximization of state variables, yields level sets of the Lyapunov function. Applying the development to comparison systems gives continuously differentiable input-to-state Lyapunov functions of networks consisting of input-to-state systems which are not necessarily monotone.
- Subject
- monotone nonlinear systems; Lyapunov functions; input-to-state stability; Perron-Frobenius theory; small-gain condition
- Identifier
- http://hdl.handle.net/1959.13/1464068
- Identifier
- uon:46904
- Identifier
- ISBN:9783030043261
- Language
- eng
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