Connection between cooperative positive systems and integral input-to-state stability of large-scale systems
We consider a class of continuous-time cooperative systems evolving on the positive orthant R + n . 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 sma...
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Veröffentlicht in: | Automatica (Oxford) 2010-06, Vol.46 (6), p.1019-1027 |
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Sprache: | eng |
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Zusammenfassung: | We consider a class of continuous-time cooperative systems evolving on the positive orthant
R
+
n
. 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, Rüffer, and Wirth (2007, in press) for large-scale interconnections of ISS systems. |
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ISSN: | 0005-1098 1873-2836 |
DOI: | 10.1016/j.automatica.2010.03.012 |