Some Local Stability Properties of an Autonomous Long Short-Term Memory Neural Network Model

Dušan M. Stipanović; Boris Murmann; Matteo Causo; Aleksandra Lekić; Vicenç Rubies Royo; Claire J. Tomlin; Edith Beigne; Sebastien Thuries; Mykhailo Zarudniev; Suzanne Lesecq

doi:10.1109/ISCAS.2018.8350958

Some Local Stability Properties of an Autonomous Long Short-Term Memory Neural Network Model

Dušan M. Stipanović
, Boris Murmann
, Matteo Causo
, Aleksandra Lekić
, Vicenç Rubies Royo
, Claire J. Tomlin
, Edith Beigne
, Sebastien Thuries
, Mykhailo Zarudniev
, Suzanne Lesecq

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

10 Citations (Scopus)

Abstract

In this paper some local stability results for an autonomous Long Short-Term Memory neural network model with respect to the origin are provided. In particular, it is shown through linearization that the local asymptotic stability conditions with respect to the origin only depend on one of the weight matrices. Simulations indicate that these local stability conditions greatly influence the behavior of the autonomous four-dimensional neural network in the region where each variable's values vary between minus one and one. Finally, some sufficient stability conditions for the nonlinear model are formulated as a convex program involving linear matrix inequalities.

Original language	English
Title of host publication	2018 IEEE International Symposium on Circuits and Systems, ISCAS 2018 - Proceedings
Publisher	IEEE
Volume	2018-May
ISBN (Electronic)	9781538648810
DOIs	https://doi.org/10.1109/ISCAS.2018.8350958
Publication status	Published - 26 Apr 2018
Externally published	Yes
Event	2018 IEEE International Symposium on Circuits and Systems, ISCAS 2018 - Florence, Italy Duration: 27 May 2018 → 30 May 2018

Conference

Conference	2018 IEEE International Symposium on Circuits and Systems, ISCAS 2018
Country/Territory	Italy
City	Florence
Period	27/05/18 → 30/05/18

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10.1109/ISCAS.2018.8350958

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Stipanović, D. M., Murmann, B., Causo, M., Lekić, A., Royo, V. R., Tomlin, C. J., Beigne, E., Thuries, S., Zarudniev, M., & Lesecq, S. (2018). Some Local Stability Properties of an Autonomous Long Short-Term Memory Neural Network Model. In 2018 IEEE International Symposium on Circuits and Systems, ISCAS 2018 - Proceedings (Vol. 2018-May). Article 8350958 IEEE. https://doi.org/10.1109/ISCAS.2018.8350958

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title = "Some Local Stability Properties of an Autonomous Long Short-Term Memory Neural Network Model",

abstract = "In this paper some local stability results for an autonomous Long Short-Term Memory neural network model with respect to the origin are provided. In particular, it is shown through linearization that the local asymptotic stability conditions with respect to the origin only depend on one of the weight matrices. Simulations indicate that these local stability conditions greatly influence the behavior of the autonomous four-dimensional neural network in the region where each variable's values vary between minus one and one. Finally, some sufficient stability conditions for the nonlinear model are formulated as a convex program involving linear matrix inequalities.",

author = "Stipanovi{\'c}, \{Du{\v s}an M.\} and Boris Murmann and Matteo Causo and Aleksandra Leki{\'c} and Royo, \{Vicen{\c c} Rubies\} and Tomlin, \{Claire J.\} and Edith Beigne and Sebastien Thuries and Mykhailo Zarudniev and Suzanne Lesecq",

year = "2018",

month = apr,

day = "26",

doi = "10.1109/ISCAS.2018.8350958",

language = "English",

volume = "2018-May",

booktitle = "2018 IEEE International Symposium on Circuits and Systems, ISCAS 2018 - Proceedings",

publisher = "IEEE",

address = "United States",

note = "2018 IEEE International Symposium on Circuits and Systems, ISCAS 2018 ; Conference date: 27-05-2018 Through 30-05-2018",

}

Stipanović, DM, Murmann, B, Causo, M, Lekić, A, Royo, VR, Tomlin, CJ, Beigne, E, Thuries, S, Zarudniev, M & Lesecq, S 2018, Some Local Stability Properties of an Autonomous Long Short-Term Memory Neural Network Model. in 2018 IEEE International Symposium on Circuits and Systems, ISCAS 2018 - Proceedings. vol. 2018-May, 8350958, IEEE, 2018 IEEE International Symposium on Circuits and Systems, ISCAS 2018, Florence, Italy, 27/05/18. https://doi.org/10.1109/ISCAS.2018.8350958

Some Local Stability Properties of an Autonomous Long Short-Term Memory Neural Network Model. / Stipanović, Dušan M.; Murmann, Boris; Causo, Matteo et al.
2018 IEEE International Symposium on Circuits and Systems, ISCAS 2018 - Proceedings. Vol. 2018-May IEEE, 2018. 8350958.

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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T1 - Some Local Stability Properties of an Autonomous Long Short-Term Memory Neural Network Model

AU - Stipanović, Dušan M.

AU - Murmann, Boris

AU - Causo, Matteo

AU - Lekić, Aleksandra

AU - Royo, Vicenç Rubies

AU - Tomlin, Claire J.

AU - Beigne, Edith

AU - Thuries, Sebastien

AU - Zarudniev, Mykhailo

AU - Lesecq, Suzanne

PY - 2018/4/26

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N2 - In this paper some local stability results for an autonomous Long Short-Term Memory neural network model with respect to the origin are provided. In particular, it is shown through linearization that the local asymptotic stability conditions with respect to the origin only depend on one of the weight matrices. Simulations indicate that these local stability conditions greatly influence the behavior of the autonomous four-dimensional neural network in the region where each variable's values vary between minus one and one. Finally, some sufficient stability conditions for the nonlinear model are formulated as a convex program involving linear matrix inequalities.

AB - In this paper some local stability results for an autonomous Long Short-Term Memory neural network model with respect to the origin are provided. In particular, it is shown through linearization that the local asymptotic stability conditions with respect to the origin only depend on one of the weight matrices. Simulations indicate that these local stability conditions greatly influence the behavior of the autonomous four-dimensional neural network in the region where each variable's values vary between minus one and one. Finally, some sufficient stability conditions for the nonlinear model are formulated as a convex program involving linear matrix inequalities.

UR - https://www.scopus.com/pages/publications/85057085883

U2 - 10.1109/ISCAS.2018.8350958

DO - 10.1109/ISCAS.2018.8350958

M3 - Conference contribution

AN - SCOPUS:85057085883

VL - 2018-May

BT - 2018 IEEE International Symposium on Circuits and Systems, ISCAS 2018 - Proceedings

PB - IEEE

T2 - 2018 IEEE International Symposium on Circuits and Systems, ISCAS 2018

Y2 - 27 May 2018 through 30 May 2018

ER -

Some Local Stability Properties of an Autonomous Long Short-Term Memory Neural Network Model

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