ℓ2-induced norm of discrete-time switched linear systems: Solutions and algorithms

Dawei Shi; Tongwen Chen

doi:10.1109/CDC.2012.6427117

ℓ₂-induced norm of discrete-time switched linear systems: Solutions and algorithms

Dawei Shi^*, Tongwen Chen

^*Corresponding author for this work

University of Alberta

Research output: Contribution to journal › Conference article › peer-review

1 Citation (Scopus)

Abstract

The ℓ₂-induced norm evaluation problem in finite-horizon for switched linear systems is considered in this paper. The contribution of the work is two-fold. First, two complete solutions are provided for the finite-horizon problem. The first solution is obtained based on a time-varying system approach, while the second one tries to characterize the worst-case switching law for the general case, which is state dependent. Second, optimization problems are formulated to identify the set of possible worst-case switching laws, based on which efficient algorithms are derived to solve the finite-horizon ℓ₂-induced norm problem for general switched linear systems. The results obtained are demonstrated by a numerical example.

Original language	English
Article number	6427117
Pages (from-to)	725-730
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
DOIs	https://doi.org/10.1109/CDC.2012.6427117
Publication status	Published - 2012
Externally published	Yes
Event	51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States Duration: 10 Dec 2012 → 13 Dec 2012

Access to Document

10.1109/CDC.2012.6427117

Cite this

@article{874f74b84d204ccabc7eebeab8d27fd3,

title = "ℓ2-induced norm of discrete-time switched linear systems: Solutions and algorithms",

abstract = "The ℓ2-induced norm evaluation problem in finite-horizon for switched linear systems is considered in this paper. The contribution of the work is two-fold. First, two complete solutions are provided for the finite-horizon problem. The first solution is obtained based on a time-varying system approach, while the second one tries to characterize the worst-case switching law for the general case, which is state dependent. Second, optimization problems are formulated to identify the set of possible worst-case switching laws, based on which efficient algorithms are derived to solve the finite-horizon ℓ2-induced norm problem for general switched linear systems. The results obtained are demonstrated by a numerical example.",

author = "Dawei Shi and Tongwen Chen",

year = "2012",

doi = "10.1109/CDC.2012.6427117",

language = "English",

pages = "725--730",

journal = "Proceedings of the IEEE Conference on Decision and Control",

issn = "0743-1546",

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

note = "51st IEEE Conference on Decision and Control, CDC 2012 ; Conference date: 10-12-2012 Through 13-12-2012",

}

TY - JOUR

T1 - ℓ2-induced norm of discrete-time switched linear systems

T2 - 51st IEEE Conference on Decision and Control, CDC 2012

AU - Shi, Dawei

AU - Chen, Tongwen

PY - 2012

Y1 - 2012

N2 - The ℓ2-induced norm evaluation problem in finite-horizon for switched linear systems is considered in this paper. The contribution of the work is two-fold. First, two complete solutions are provided for the finite-horizon problem. The first solution is obtained based on a time-varying system approach, while the second one tries to characterize the worst-case switching law for the general case, which is state dependent. Second, optimization problems are formulated to identify the set of possible worst-case switching laws, based on which efficient algorithms are derived to solve the finite-horizon ℓ2-induced norm problem for general switched linear systems. The results obtained are demonstrated by a numerical example.

AB - The ℓ2-induced norm evaluation problem in finite-horizon for switched linear systems is considered in this paper. The contribution of the work is two-fold. First, two complete solutions are provided for the finite-horizon problem. The first solution is obtained based on a time-varying system approach, while the second one tries to characterize the worst-case switching law for the general case, which is state dependent. Second, optimization problems are formulated to identify the set of possible worst-case switching laws, based on which efficient algorithms are derived to solve the finite-horizon ℓ2-induced norm problem for general switched linear systems. The results obtained are demonstrated by a numerical example.

UR - http://www.scopus.com/inward/record.url?scp=84874267266&partnerID=8YFLogxK

U2 - 10.1109/CDC.2012.6427117

DO - 10.1109/CDC.2012.6427117

M3 - Conference article

AN - SCOPUS:84874267266

SN - 0743-1546

SP - 725

EP - 730

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

M1 - 6427117

Y2 - 10 December 2012 through 13 December 2012

ER -

ℓ₂-induced norm of discrete-time switched linear systems: Solutions and algorithms

Abstract

Access to Document

Other files and links

Fingerprint

Cite this