Extension of State Space and Lyapunov Matrices

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Extension of State Space and Lyapunov Matrices. / Aliseyko, Alexey N.

In: IEEE Transactions on Automatic Control, Vol. 66, No. 4, 9095390, 04.2021, p. 1771-1777.

Research output: Contribution to journal › Article › peer-review

Author

Aliseyko, Alexey N. / Extension of State Space and Lyapunov Matrices. In: IEEE Transactions on Automatic Control. 2021 ; Vol. 66, No. 4. pp. 1771-1777.

BibTeX

@article{1a631ce34d484a7fb6e6a7d7d069dbed,

title = "Extension of State Space and Lyapunov Matrices",

abstract = "One of the main problems in the application of the theory of Lyapunov-Krasovskii functionals is the construction of corresponding Lyapunov matrices. Recently, it was noted that systems with distributed delay and exponential kernel may be rewritten by the introduction of auxiliary variables as systems with one delay. A suggestion was made that one can use the Lyapunov matrix of the latter system to obtain the Lyapunov matrix of the original system. In this article, we establish precise relationships between these two systems and their Lyapunov matrices. We show that if there exists a Lyapunov matrix of the extended system then it can be used to compute a Lyapunov matrix of the nominal system. We demonstrate that this method fails for certain systems and establish necessary and sufficient conditions for the extended system to admit a Lyapunov matrix. ",

keywords = "Lyapunov matrices, Lyapunov-Krasovskii functionals, stability, time-delay systems",

author = "Aliseyko, {Alexey N.}",

year = "2021",

month = apr,

doi = "10.1109/tac.2020.2995404",

language = "English",

volume = "66",

pages = "1771--1777",

journal = "IEEE Transactions on Automatic Control",

issn = "0018-9286",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "4",

}

RIS

TY - JOUR

T1 - Extension of State Space and Lyapunov Matrices

AU - Aliseyko, Alexey N.

PY - 2021/4

Y1 - 2021/4

N2 - One of the main problems in the application of the theory of Lyapunov-Krasovskii functionals is the construction of corresponding Lyapunov matrices. Recently, it was noted that systems with distributed delay and exponential kernel may be rewritten by the introduction of auxiliary variables as systems with one delay. A suggestion was made that one can use the Lyapunov matrix of the latter system to obtain the Lyapunov matrix of the original system. In this article, we establish precise relationships between these two systems and their Lyapunov matrices. We show that if there exists a Lyapunov matrix of the extended system then it can be used to compute a Lyapunov matrix of the nominal system. We demonstrate that this method fails for certain systems and establish necessary and sufficient conditions for the extended system to admit a Lyapunov matrix.

AB - One of the main problems in the application of the theory of Lyapunov-Krasovskii functionals is the construction of corresponding Lyapunov matrices. Recently, it was noted that systems with distributed delay and exponential kernel may be rewritten by the introduction of auxiliary variables as systems with one delay. A suggestion was made that one can use the Lyapunov matrix of the latter system to obtain the Lyapunov matrix of the original system. In this article, we establish precise relationships between these two systems and their Lyapunov matrices. We show that if there exists a Lyapunov matrix of the extended system then it can be used to compute a Lyapunov matrix of the nominal system. We demonstrate that this method fails for certain systems and establish necessary and sufficient conditions for the extended system to admit a Lyapunov matrix.

KW - Lyapunov matrices

KW - Lyapunov-Krasovskii functionals

KW - stability

KW - time-delay systems

UR - http://www.scopus.com/inward/record.url?scp=85103470047&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/eb577b18-13e7-3fa0-8a30-ef97af71550a/

U2 - 10.1109/tac.2020.2995404

DO - 10.1109/tac.2020.2995404

M3 - Article

AN - SCOPUS:85103470047

VL - 66

SP - 1771

EP - 1777

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 4

M1 - 9095390

ER -

ID: 76785498