A generalization of linear positive systems

Eyal Weiss; Michael Margaliot

doi:10.1109/med.2019.8798547

A generalization of linear positive systems

Eyal Weiss, Michael Margaliot

Tel Aviv University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Scopus citations

Abstract

The dynamics of linear positive systems maps the positive orthant to itself. Namely, it maps a set of vectors with zero sign variations to itself. Hence, a natural question is: what linear systems map the set of vectors with k sign variations to itself? To address this question we use tools from the theory of cooperative dynamical systems and the theory of totally positive matrices. Our approach yields a generalization of positive linear systems called k-positive linear systems, which reduces to positive systems for k=1. We show an application of this new class of systems to the analysis of invariant sets in nonlinear time-varying dynamical systems.

Original language	English
Title of host publication	27th Mediterranean Conference on Control and Automation, MED 2019 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	340-345
Number of pages	6
ISBN (Electronic)	9781728128030
DOIs	https://doi.org/10.1109/med.2019.8798547
State	Published - Jul 2019
Externally published	Yes
Event	27th Mediterranean Conference on Control and Automation, MED 2019 - Akko, Israel Duration: 1 Jul 2019 → 4 Jul 2019

Publication series

Name	27th Mediterranean Conference on Control and Automation, MED 2019 - Proceedings

Conference

Conference	27th Mediterranean Conference on Control and Automation, MED 2019
Country/Territory	Israel
City	Akko
Period	1/07/19 → 4/07/19

Bibliographical note

Publisher Copyright:
© 2019 IEEE.

Funding

This research was partially supported by research grants from the Israel Science Foundation and the Binational Science Foundation. EW is with the School of Elec. Eng., Tel Aviv University, Israel. MM (Corresponding Author) is with the School of Elec. Eng. and the Sagol School of Neuroscience, Tel-Aviv University, Tel-Aviv 69978, Israel.

Funders	Funder number
United States-Israel Binational Science Foundation
Israel Science Foundation

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10.1109/med.2019.8798547

Cite this

Weiss, E., & Margaliot, M. (2019). A generalization of linear positive systems. In 27th Mediterranean Conference on Control and Automation, MED 2019 - Proceedings (pp. 340-345). Article 8798547 (27th Mediterranean Conference on Control and Automation, MED 2019 - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/med.2019.8798547

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year = "2019",

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doi = "10.1109/med.2019.8798547",

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Weiss, E & Margaliot, M 2019, A generalization of linear positive systems. in 27th Mediterranean Conference on Control and Automation, MED 2019 - Proceedings., 8798547, 27th Mediterranean Conference on Control and Automation, MED 2019 - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 340-345, 27th Mediterranean Conference on Control and Automation, MED 2019, Akko, Israel, 1/07/19. https://doi.org/10.1109/med.2019.8798547

A generalization of linear positive systems. / Weiss, Eyal; Margaliot, Michael.
27th Mediterranean Conference on Control and Automation, MED 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. p. 340-345 8798547 (27th Mediterranean Conference on Control and Automation, MED 2019 - Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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A generalization of linear positive systems

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