Publication

Novel Gramians for linear semistable systems

Cheng, X. & Scherpen, J. M. A., May-2020, In : Automatica. 115, 9 p., 108911.

Research output: Contribution to journalArticleAcademicpeer-review

APA

Cheng, X., & Scherpen, J. M. A. (2020). Novel Gramians for linear semistable systems. Automatica, 115, [108911]. https://doi.org/10.1016/j.automatica.2020.108911

Author

Cheng, Xiaodong ; Scherpen, Jacquelien M. A. / Novel Gramians for linear semistable systems. In: Automatica. 2020 ; Vol. 115.

Harvard

Cheng, X & Scherpen, JMA 2020, 'Novel Gramians for linear semistable systems', Automatica, vol. 115, 108911. https://doi.org/10.1016/j.automatica.2020.108911

Standard

Novel Gramians for linear semistable systems. / Cheng, Xiaodong; Scherpen, Jacquelien M. A.

In: Automatica, Vol. 115, 108911, 05.2020.

Research output: Contribution to journalArticleAcademicpeer-review

Vancouver

Cheng X, Scherpen JMA. Novel Gramians for linear semistable systems. Automatica. 2020 May;115. 108911. https://doi.org/10.1016/j.automatica.2020.108911


BibTeX

@article{2f054bb32b4543a5a224742c9a3676bb,
title = "Novel Gramians for linear semistable systems",
abstract = "In this paper, the notions of pseudo Gramians are introduced for linear time-invariant semistable systems, which allow multiple semisimple poles at the origin. The proposed Gramians are the generalizations of standard Gramian matrices defined for asymptotically stable systems, and they can be computed by a set of Lyapunov equations. Furthermore, it is shown that the controllability and observability of a semistable system are indicated by the ranks of the pseudo Gramians, and the controllability and observability energy functions are also characterized using the pseudo Gramians. Additionally, the H2-norm and H∞-norm of a semistable system are analyzed, and then the results are used for the model reduction of semistable systems. Finally, the effectiveness of the methods is illustrated by an example of a gene regulation network.",
keywords = "Gramian matrix, Model reduction, Semistability, Linear system, Controllability and observability, MODEL-REDUCTION, CONTROLLABILITY, NETWORKS",
author = "Xiaodong Cheng and Scherpen, {Jacquelien M. A.}",
year = "2020",
month = may,
doi = "10.1016/j.automatica.2020.108911",
language = "English",
volume = "115",
journal = "Automatica",
issn = "1873-2836",
publisher = "PERGAMON-ELSEVIER SCIENCE LTD",

}

RIS

TY - JOUR

T1 - Novel Gramians for linear semistable systems

AU - Cheng, Xiaodong

AU - Scherpen, Jacquelien M. A.

PY - 2020/5

Y1 - 2020/5

N2 - In this paper, the notions of pseudo Gramians are introduced for linear time-invariant semistable systems, which allow multiple semisimple poles at the origin. The proposed Gramians are the generalizations of standard Gramian matrices defined for asymptotically stable systems, and they can be computed by a set of Lyapunov equations. Furthermore, it is shown that the controllability and observability of a semistable system are indicated by the ranks of the pseudo Gramians, and the controllability and observability energy functions are also characterized using the pseudo Gramians. Additionally, the H2-norm and H∞-norm of a semistable system are analyzed, and then the results are used for the model reduction of semistable systems. Finally, the effectiveness of the methods is illustrated by an example of a gene regulation network.

AB - In this paper, the notions of pseudo Gramians are introduced for linear time-invariant semistable systems, which allow multiple semisimple poles at the origin. The proposed Gramians are the generalizations of standard Gramian matrices defined for asymptotically stable systems, and they can be computed by a set of Lyapunov equations. Furthermore, it is shown that the controllability and observability of a semistable system are indicated by the ranks of the pseudo Gramians, and the controllability and observability energy functions are also characterized using the pseudo Gramians. Additionally, the H2-norm and H∞-norm of a semistable system are analyzed, and then the results are used for the model reduction of semistable systems. Finally, the effectiveness of the methods is illustrated by an example of a gene regulation network.

KW - Gramian matrix

KW - Model reduction

KW - Semistability

KW - Linear system

KW - Controllability and observability

KW - MODEL-REDUCTION

KW - CONTROLLABILITY

KW - NETWORKS

U2 - 10.1016/j.automatica.2020.108911

DO - 10.1016/j.automatica.2020.108911

M3 - Article

VL - 115

JO - Automatica

JF - Automatica

SN - 1873-2836

M1 - 108911

ER -

ID: 127071665