Robust H2 control of uncertain discrete-time linear systems with periodically time-varying memory state-feedback

Yoshio Ebihara

doi:10.1109/CACSD.2010.5612782

Robust H₂ control of uncertain discrete-time linear systems with periodically time-varying memory state-feedback

Yoshio Ebihara

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

This study is concerned with the synthesis of periodically time-varying memory state-feedback controllers (PTVMSFCs) for discrete-time linear systems. In our preceding studies, we have already established a solid theoretical basis for the LMI-based (robust) H_∞-PTVMSFCs synthesis, and the goal of this paper is to extend those results to the H₂ performance criterion. In the H₂ case, the main difficulty stems from the fact that we have to ensure the existence of common auxiliary variables for multiple LMI conditions that are related to the Lyapunov inequality and inequalities for bounding traces that characterize the H₂ norm. We can indeed overcome this difficulty and derive a necessary and sufficient LMI condition for the optimal H₂-PTVMSFC synthesis. Based on this result, we also consider robust H₂-PTVMSFC synthesis for polytopictype uncertain LTI systems.

Original language	English
Title of host publication	2010 IEEE International Symposium on Computer-Aided Control System Design, CACSD 2010
Pages	357-362
Number of pages	6
DOIs	https://doi.org/10.1109/CACSD.2010.5612782
Publication status	Published - 2010
Externally published	Yes
Event	2010 IEEE International Symposium on Computer-Aided Control System Design, CACSD 2010 - Yokohama, Japan Duration: Sept 8 2010 → Sept 10 2010

Publication series

Name	Proceedings of the IEEE International Symposium on Computer-Aided Control System Design

Other

Other	2010 IEEE International Symposium on Computer-Aided Control System Design, CACSD 2010
Country/Territory	Japan
City	Yokohama
Period	9/8/10 → 9/10/10

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Computer Science Applications
Control and Optimization

Access to Document

10.1109/CACSD.2010.5612782

Cite this

Ebihara, Y. (2010). Robust H₂ control of uncertain discrete-time linear systems with periodically time-varying memory state-feedback. In 2010 IEEE International Symposium on Computer-Aided Control System Design, CACSD 2010 (pp. 357-362). Article 5612782 (Proceedings of the IEEE International Symposium on Computer-Aided Control System Design). https://doi.org/10.1109/CACSD.2010.5612782

Robust H₂ control of uncertain discrete-time linear systems with periodically time-varying memory state-feedback. / Ebihara, Yoshio.
2010 IEEE International Symposium on Computer-Aided Control System Design, CACSD 2010. 2010. p. 357-362 5612782 (Proceedings of the IEEE International Symposium on Computer-Aided Control System Design).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Ebihara, Y 2010, Robust H₂ control of uncertain discrete-time linear systems with periodically time-varying memory state-feedback. in 2010 IEEE International Symposium on Computer-Aided Control System Design, CACSD 2010., 5612782, Proceedings of the IEEE International Symposium on Computer-Aided Control System Design, pp. 357-362, 2010 IEEE International Symposium on Computer-Aided Control System Design, CACSD 2010, Yokohama, Japan, 9/8/10. https://doi.org/10.1109/CACSD.2010.5612782

@inproceedings{271bc9f0c22145feb47d91f0d186b3bb,

title = "Robust H2 control of uncertain discrete-time linear systems with periodically time-varying memory state-feedback",

abstract = "This study is concerned with the synthesis of periodically time-varying memory state-feedback controllers (PTVMSFCs) for discrete-time linear systems. In our preceding studies, we have already established a solid theoretical basis for the LMI-based (robust) H∞-PTVMSFCs synthesis, and the goal of this paper is to extend those results to the H2 performance criterion. In the H2 case, the main difficulty stems from the fact that we have to ensure the existence of common auxiliary variables for multiple LMI conditions that are related to the Lyapunov inequality and inequalities for bounding traces that characterize the H2 norm. We can indeed overcome this difficulty and derive a necessary and sufficient LMI condition for the optimal H2-PTVMSFC synthesis. Based on this result, we also consider robust H2-PTVMSFC synthesis for polytopictype uncertain LTI systems.",

author = "Yoshio Ebihara",

year = "2010",

doi = "10.1109/CACSD.2010.5612782",

language = "English",

isbn = "9781424453542",

series = "Proceedings of the IEEE International Symposium on Computer-Aided Control System Design",

pages = "357--362",

booktitle = "2010 IEEE International Symposium on Computer-Aided Control System Design, CACSD 2010",

note = "2010 IEEE International Symposium on Computer-Aided Control System Design, CACSD 2010 ; Conference date: 08-09-2010 Through 10-09-2010",

}

TY - GEN

T1 - Robust H2 control of uncertain discrete-time linear systems with periodically time-varying memory state-feedback

AU - Ebihara, Yoshio

PY - 2010

Y1 - 2010

N2 - This study is concerned with the synthesis of periodically time-varying memory state-feedback controllers (PTVMSFCs) for discrete-time linear systems. In our preceding studies, we have already established a solid theoretical basis for the LMI-based (robust) H∞-PTVMSFCs synthesis, and the goal of this paper is to extend those results to the H2 performance criterion. In the H2 case, the main difficulty stems from the fact that we have to ensure the existence of common auxiliary variables for multiple LMI conditions that are related to the Lyapunov inequality and inequalities for bounding traces that characterize the H2 norm. We can indeed overcome this difficulty and derive a necessary and sufficient LMI condition for the optimal H2-PTVMSFC synthesis. Based on this result, we also consider robust H2-PTVMSFC synthesis for polytopictype uncertain LTI systems.

AB - This study is concerned with the synthesis of periodically time-varying memory state-feedback controllers (PTVMSFCs) for discrete-time linear systems. In our preceding studies, we have already established a solid theoretical basis for the LMI-based (robust) H∞-PTVMSFCs synthesis, and the goal of this paper is to extend those results to the H2 performance criterion. In the H2 case, the main difficulty stems from the fact that we have to ensure the existence of common auxiliary variables for multiple LMI conditions that are related to the Lyapunov inequality and inequalities for bounding traces that characterize the H2 norm. We can indeed overcome this difficulty and derive a necessary and sufficient LMI condition for the optimal H2-PTVMSFC synthesis. Based on this result, we also consider robust H2-PTVMSFC synthesis for polytopictype uncertain LTI systems.

UR - http://www.scopus.com/inward/record.url?scp=78649895308&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78649895308&partnerID=8YFLogxK

U2 - 10.1109/CACSD.2010.5612782

DO - 10.1109/CACSD.2010.5612782

M3 - Conference contribution

AN - SCOPUS:78649895308

SN - 9781424453542

T3 - Proceedings of the IEEE International Symposium on Computer-Aided Control System Design

SP - 357

EP - 362

BT - 2010 IEEE International Symposium on Computer-Aided Control System Design, CACSD 2010

T2 - 2010 IEEE International Symposium on Computer-Aided Control System Design, CACSD 2010

Y2 - 8 September 2010 through 10 September 2010

ER -