D-Stability and Delay-Independent Stability of Homogeneous Cooperative Systems

Bokharaie, VS; Mason, O; Verwoerd, M

doi:10.1109/TAC.2010.2076334

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D-Stability and Delay-Independent Stability of Homogeneous Cooperative Systems

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https://ieeexplore.ieee.org/document/5570915
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Bokharaie, V., Mason, O., & Verwoerd, M. (2010). D-Stability and Delay-Independent Stability of Homogeneous Cooperative Systems. IEEE Transactions on Automatic Control, 55(12), 2882-2885. doi:10.1109/TAC.2010.2076334.

Cite as: https://hdl.handle.net/21.11116/0000-0002-689A-C

Abstract

We introduce a nonlinear definition of D-stability, extending the usual concept for positive linear time-invariant systems. We show that globally asymptotically stable, cooperative systems, homogeneous of any order with respect to arbitrary dilation maps are D-stable. We also prove a strong stability result for delayed cooperative homogeneous systems. Finally, we show that both of these results also hold for planar cooperative systems without the restriction of homogeneity.