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Observations on the stability properties of cooperative systems. (English) Zbl 1161.93021

Summary: We extend two fundamental properties of positive linear time-invariant systems to homogeneous cooperative systems. Specifically, we demonstrate that such systems are \(D\)-stable, meaning that global asymptotic stability is preserved under diagonal scaling. We also show that a delayed homogeneous cooperative system is Globally Asymptotically Stable (GAS) for all non-negative delays if and only if the system is GAS for zero delay.

MSC:

93D20 Asymptotic stability in control theory
93A14 Decentralized systems
93C15 Control/observation systems governed by ordinary differential equations
93C05 Linear systems in control theory
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