- Title
- Small-gain stability theorems for positive Lur'e inclusions
- Creator
- Guiver, Chris; Logemann, Hartmut; Rüffer, Björn
- Relation
- ARC.DP160102138
- Relation
- Positivity Vol. 23, p. 249-289
- Publisher Link
- http://dx.doi.org/10.1007/s11117-018-0605-2
- Publisher
- Birkhaeuser Science
- Resource Type
- journal article
- Date
- 2019
- Description
- Stability results are presented for a class of differential and difference inclusions, so-called positive Lur'e inclusions which arise, for example, as the feedback interconnection of a linear positive system with a positive set-valued static nonlinearity. We formulate sufficient conditions in terms of weighted one-norms, reminiscent of the small-gain condition, which ensure that the zero equilibrium enjoys various global stability properties, including asymptotic and exponential stability. We also consider input-to-state stability, familiar from nonlinear control theory, in the context of forced positive Lur'e inclusions. Typical for the study of positive systems, our analysis benefits from comparison arguments and linear Lyapunov functions. The theory is illustrated with examples.
- Subject
- differential inclusion; exponential stability; input-to-state stability; Lur'e systems; population biology; positive systems
- Identifier
- http://hdl.handle.net/1959.13/1422375
- Identifier
- uon:37821
- Identifier
- ISSN:1385-1292
- Rights
- Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
- Language
- eng
- Full Text
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