- Title
- Connection between cooperative positive systems and integral input-to-state stability of large-scale systems
- Creator
- Ruffer, Björn S.; Kellett, Christopher M.; Weller, Steven R.
- Relation
- Automatica Vol. 46, Issue 6, p. 1019-1027
- Publisher Link
- http://dx.doi.org/10.1016/j.automatica.2010.03.012
- Publisher
- Elsevier
- Resource Type
- journal article
- Date
- 2010
- Description
- We consider a class of continuous-time cooperative systems evolving on the positive orthant ℝⁿ₊. We show that if the origin is globally attractive, then it is also globally stable and, furthermore, there exists an unbounded invariant manifold where trajectories strictly decay. This leads to a small-gain-type condition which is sufficient for global asymptotic stability (GAS) of the origin. We establish the following connection to large-scale interconnections of (integral) input-to-state stable (ISS) subsystems: If the cooperative system is (integral) ISS, and arises as a comparison system associated with a large-scale interconnection of (i)ISS systems, then the composite nominal system is also (i)ISS. We provide a criterion in terms of a Lyapunov function for (integral) input-to-state stability of the comparison system. Furthermore, we show that if a small-gain condition holds then the classes of systems participating in the large-scale interconnection are restricted in the sense that certain iISS systems cannot occur. Moreover, this small-gain condition is essentially the same as the one obtained previously by [Dashkovskiy et al., 2007] and [Dashkovskiy et al., in press] for large-scale interconnections of ISS systems.
- Subject
- nonlinear systems; dissipation inequalities; comparison system; monotone systems; integral input-to-state stability (iISS); Lyapunov function; small-gain condition; nonlinear gain
- Identifier
- http://hdl.handle.net/1959.13/930288
- Identifier
- uon:10809
- Identifier
- ISSN:0005-1098
- Language
- eng
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