Differentially positive systems
IEEE Transactions on Automatic Control
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Forni, F., & Sepulchre, R. (2015). Differentially positive systems. IEEE Transactions on Automatic Control, 61 346-359. https://doi.org/10.1109/TAC.2015.2437523
The paper introduces and studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. A generalization of Perron Frobenius theory is developed in this differential framework to show that the property induces a (conal) order that strongly constrains the asymptotic behavior of solutions. The results illustrate that behaviors constrained by local order properties extend beyond the well-studied class of linear positive systems and monotone systems, which both require a constant cone field and a linear state space.
The research was supported by the Fund for Scientific Research FNRS and by the Engineering and Physical Sciences Research Council under Grant EP/G066477/1.
ECH2020 EUROPEAN RESEARCH COUNCIL (ERC) (670645)
External DOI: https://doi.org/10.1109/TAC.2015.2437523
This record's URL: https://www.repository.cam.ac.uk/handle/1810/251266