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

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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

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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.",

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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

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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.

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Y2 - 6 July 2014 through 11 July 2014

ER -

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

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