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Distance to the nearest stable Metzler matrix

Anderson, James (2017) Distance to the nearest stable Metzler matrix. In: 2017 IEEE 56th Annual Conference on Decision and Control (CDC). IEEE , Piscataway, NJ, pp. 6567-6572. ISBN 978-1-5090-2873-3.

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This paper considers the non-convex problem of finding the nearest Metzler matrix to a given possibly unstable matrix. Linear systems whose state vector evolves according to a Metzler matrix have many desirable properties in analysis and control with regard to scalability. This motivates the question, how close (in the Frobenius norm of coefficients) to the nearest Metzler matrix are we? Dropping the Metzler constraint, this problem has recently been studied using the theory of dissipative Hamiltonian (DH) systems, which provide a helpful characterization of the feasible set of stable matrices. This work uses the DH theory to provide a block coordinate descent algorithm consisting of a quadratic program with favourable structural properties and a semidefinite program for which recent diagonal dominance results can be used to improve tractability.

Item Type:Book Section
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Anderson, James0000-0002-2832-8396
Additional Information:© 2017 IEEE. This work was funded by NSF CNS award 1545096, ECCS award 1619352, CCF award 1637598, and ARPA-E award GRID DATA. I would like to thank Riley Murray at Caltech for many helpful discussions regarding the dual problem. The outcome of which is currently being written up.
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Record Number:CaltechAUTHORS:20180301-102353949
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Official Citation:J. Anderson, "Distance to the nearest stable Metzler matrix," 2017 IEEE 56th Annual Conference on Decision and Control (CDC), Melbourne, VIC, 2017, pp. 6567-6572. doi: 10.1109/CDC.2017.8264649. URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85036
Deposited By: Tony Diaz
Deposited On:01 Mar 2018 20:29
Last Modified:03 Oct 2019 19:25

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