Robust stability analysis of PD type single input interval type-2 fuzzy control systems

Tufan Kumbasar

doi:10.1109/FUZZ-IEEE.2014.6891616

Robust stability analysis of PD type single input interval type-2 fuzzy control systems

Tufan Kumbasar^*

^*Corresponding author for this work

Department of Control and Automation Engineering

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

12 Citations (Scopus)

Abstract

In this paper, the robust stability of a PD type Single input Interval Type-2 Fuzzy Logic Controller (SIT2-FLC) structure will be examined via the well-known Popov criterion and Lyapunov's direct method approach. Since a closed form formulation of the SIT2-FLC output is possible, the type-2 fuzzy functional mapping is analyzed in a two dimensional domain. Thus, mathematical derivations are presented to show that type-2 fuzzy functional mapping is a symmetrical function and always sector bounded. Consequently, the type-2 fuzzy system can be transformed into a perturbed Lur'e system to examine its robust stability. It has been proven that the stability of the PD type SIT2-FLC system is guaranteed with the aids of the Popov-Lyapunov method. A robustness measure of the type-2 fuzzy control system is also presented to give the bound of allowable uncertainties/ nonlinearities of the control system. Moreover, if this bound is known, the exact region of stability of the type-2 fuzzy system can be found since SIT2-FLC output can be presented in a closed form. An illustrate example is presented to demonstrate the robust stability analysis of the PD type SIT2-FLC system.

Original language	English
Title of host publication	Proceedings of the 2014 IEEE International Conference on Fuzzy Systems, FUZZ-IEEE
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	634-639
Number of pages	6
ISBN (Electronic)	9781479920723
DOIs	https://doi.org/10.1109/FUZZ-IEEE.2014.6891616
Publication status	Published - 4 Sept 2014
Event	2014 IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2014 - Beijing, China Duration: 6 Jul 2014 → 11 Jul 2014

Publication series

Name	IEEE International Conference on Fuzzy Systems
ISSN (Print)	1098-7584

Conference

Conference	2014 IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2014
Country/Territory	China
City	Beijing
Period	6/07/14 → 11/07/14

Bibliographical note

Publisher Copyright:
© 2014 IEEE.

Keywords

Interval type-2 fuzzy logic controllers
Lur'e system
Robust stability

Access to Document

10.1109/FUZZ-IEEE.2014.6891616

Cite this

Kumbasar, T. (2014). Robust stability analysis of PD type single input interval type-2 fuzzy control systems. In Proceedings of the 2014 IEEE International Conference on Fuzzy Systems, FUZZ-IEEE (pp. 634-639). Article 6891616 (IEEE International Conference on Fuzzy Systems). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/FUZZ-IEEE.2014.6891616

@inproceedings{e4ee4ef5bf094be7b9ccd91abea3ee5a,

title = "Robust stability analysis of PD type single input interval type-2 fuzzy control systems",

abstract = "In this paper, the robust stability of a PD type Single input Interval Type-2 Fuzzy Logic Controller (SIT2-FLC) structure will be examined via the well-known Popov criterion and Lyapunov's direct method approach. Since a closed form formulation of the SIT2-FLC output is possible, the type-2 fuzzy functional mapping is analyzed in a two dimensional domain. Thus, mathematical derivations are presented to show that type-2 fuzzy functional mapping is a symmetrical function and always sector bounded. Consequently, the type-2 fuzzy system can be transformed into a perturbed Lur'e system to examine its robust stability. It has been proven that the stability of the PD type SIT2-FLC system is guaranteed with the aids of the Popov-Lyapunov method. A robustness measure of the type-2 fuzzy control system is also presented to give the bound of allowable uncertainties/ nonlinearities of the control system. Moreover, if this bound is known, the exact region of stability of the type-2 fuzzy system can be found since SIT2-FLC output can be presented in a closed form. An illustrate example is presented to demonstrate the robust stability analysis of the PD type SIT2-FLC system.",

keywords = "Interval type-2 fuzzy logic controllers, Lur'e system, Robust stability",

author = "Tufan Kumbasar",

note = "Publisher Copyright: {\textcopyright} 2014 IEEE.; 2014 IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2014 ; Conference date: 06-07-2014 Through 11-07-2014",

year = "2014",

month = sep,

day = "4",

doi = "10.1109/FUZZ-IEEE.2014.6891616",

language = "English",

series = "IEEE International Conference on Fuzzy Systems",

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

pages = "634--639",

booktitle = "Proceedings of the 2014 IEEE International Conference on Fuzzy Systems, FUZZ-IEEE",

address = "United States",

}

Kumbasar, T 2014, Robust stability analysis of PD type single input interval type-2 fuzzy control systems. in Proceedings of the 2014 IEEE International Conference on Fuzzy Systems, FUZZ-IEEE., 6891616, IEEE International Conference on Fuzzy Systems, Institute of Electrical and Electronics Engineers Inc., pp. 634-639, 2014 IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2014, Beijing, China, 6/07/14. https://doi.org/10.1109/FUZZ-IEEE.2014.6891616

Robust stability analysis of PD type single input interval type-2 fuzzy control systems. / Kumbasar, Tufan.
Proceedings of the 2014 IEEE International Conference on Fuzzy Systems, FUZZ-IEEE. Institute of Electrical and Electronics Engineers Inc., 2014. p. 634-639 6891616 (IEEE International Conference on Fuzzy Systems).

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

TY - GEN

T1 - Robust stability analysis of PD type single input interval type-2 fuzzy control systems

AU - Kumbasar, Tufan

PY - 2014/9/4

Y1 - 2014/9/4

N2 - In this paper, the robust stability of a PD type Single input Interval Type-2 Fuzzy Logic Controller (SIT2-FLC) structure will be examined via the well-known Popov criterion and Lyapunov's direct method approach. Since a closed form formulation of the SIT2-FLC output is possible, the type-2 fuzzy functional mapping is analyzed in a two dimensional domain. Thus, mathematical derivations are presented to show that type-2 fuzzy functional mapping is a symmetrical function and always sector bounded. Consequently, the type-2 fuzzy system can be transformed into a perturbed Lur'e system to examine its robust stability. It has been proven that the stability of the PD type SIT2-FLC system is guaranteed with the aids of the Popov-Lyapunov method. A robustness measure of the type-2 fuzzy control system is also presented to give the bound of allowable uncertainties/ nonlinearities of the control system. Moreover, if this bound is known, the exact region of stability of the type-2 fuzzy system can be found since SIT2-FLC output can be presented in a closed form. An illustrate example is presented to demonstrate the robust stability analysis of the PD type SIT2-FLC system.

AB - In this paper, the robust stability of a PD type Single input Interval Type-2 Fuzzy Logic Controller (SIT2-FLC) structure will be examined via the well-known Popov criterion and Lyapunov's direct method approach. Since a closed form formulation of the SIT2-FLC output is possible, the type-2 fuzzy functional mapping is analyzed in a two dimensional domain. Thus, mathematical derivations are presented to show that type-2 fuzzy functional mapping is a symmetrical function and always sector bounded. Consequently, the type-2 fuzzy system can be transformed into a perturbed Lur'e system to examine its robust stability. It has been proven that the stability of the PD type SIT2-FLC system is guaranteed with the aids of the Popov-Lyapunov method. A robustness measure of the type-2 fuzzy control system is also presented to give the bound of allowable uncertainties/ nonlinearities of the control system. Moreover, if this bound is known, the exact region of stability of the type-2 fuzzy system can be found since SIT2-FLC output can be presented in a closed form. An illustrate example is presented to demonstrate the robust stability analysis of the PD type SIT2-FLC system.

KW - Interval type-2 fuzzy logic controllers

KW - Lur'e system

KW - Robust stability

UR - http://www.scopus.com/inward/record.url?scp=84912553626&partnerID=8YFLogxK

U2 - 10.1109/FUZZ-IEEE.2014.6891616

DO - 10.1109/FUZZ-IEEE.2014.6891616

M3 - Conference contribution

AN - SCOPUS:84912553626

T3 - IEEE International Conference on Fuzzy Systems

SP - 634

EP - 639

BT - Proceedings of the 2014 IEEE International Conference on Fuzzy Systems, FUZZ-IEEE

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2014 IEEE International Conference on Fuzzy Systems, FUZZ-IEEE 2014

Y2 - 6 July 2014 through 11 July 2014

ER -

Robust stability analysis of PD type single input interval type-2 fuzzy control systems

Abstract

Publication series

Conference

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this