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 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 tha...

• Type: Journal
• Year: 2010
• Where: AUTOMATICA
• Authors: Björn Rüffer, Christopher M. Kellett, Steven R. Weller
• Keywords: Artificial Intelligence, AUTOMATICA 2010, Large-scale Interconnections, Small-gain Condition, Systems