A new stability region analysis of continuous-time Takagi-Sugeno fuzzy systems using fuzzy Lyapunov functions

Dong Hwan Lee, Jin Bae Park, Young Hoon Joo, Myung Hwan Tak

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we propose a new sufficient condition in the form of eigenvalue problem (EVP) for assessing the stability of continuous-time Takagi-Sugeno (T-S) fuzzy systems and estimating the domain of attraction (DA) based on fuzzy Lyapunov functions (FLFs). In order to deal with the time-derivatives of the fuzzy weighting functions (TDFWFs) in the Lyapunov inequality, the existing conditions consider the upper bound on each TDFWF's absolute value. The main result of this paper is derived considering an inequality constraint of a nonlinear function depending quadratically on the fuzzy weighting functions. Finally, an example is given to demonstrate the effectiveness and validity of the proposed approach.

Original languageEnglish
Title of host publicationICCAS 2011 - 2011 11th International Conference on Control, Automation and Systems
Pages1652-1655
Number of pages4
Publication statusPublished - 2011 Dec 1
Event2011 11th International Conference on Control, Automation and Systems, ICCAS 2011 - Gyeonggi-do, Korea, Republic of
Duration: 2011 Oct 262011 Oct 29

Other

Other2011 11th International Conference on Control, Automation and Systems, ICCAS 2011
CountryKorea, Republic of
CityGyeonggi-do
Period11/10/2611/10/29

Fingerprint

Fuzzy systems
Lyapunov functions
Derivatives

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Computer Science Applications
  • Control and Systems Engineering
  • Electrical and Electronic Engineering

Cite this

Lee, D. H., Park, J. B., Joo, Y. H., & Tak, M. H. (2011). A new stability region analysis of continuous-time Takagi-Sugeno fuzzy systems using fuzzy Lyapunov functions. In ICCAS 2011 - 2011 11th International Conference on Control, Automation and Systems (pp. 1652-1655). [6106260]
Lee, Dong Hwan ; Park, Jin Bae ; Joo, Young Hoon ; Tak, Myung Hwan. / A new stability region analysis of continuous-time Takagi-Sugeno fuzzy systems using fuzzy Lyapunov functions. ICCAS 2011 - 2011 11th International Conference on Control, Automation and Systems. 2011. pp. 1652-1655
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abstract = "In this paper, we propose a new sufficient condition in the form of eigenvalue problem (EVP) for assessing the stability of continuous-time Takagi-Sugeno (T-S) fuzzy systems and estimating the domain of attraction (DA) based on fuzzy Lyapunov functions (FLFs). In order to deal with the time-derivatives of the fuzzy weighting functions (TDFWFs) in the Lyapunov inequality, the existing conditions consider the upper bound on each TDFWF's absolute value. The main result of this paper is derived considering an inequality constraint of a nonlinear function depending quadratically on the fuzzy weighting functions. Finally, an example is given to demonstrate the effectiveness and validity of the proposed approach.",
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Lee, DH, Park, JB, Joo, YH & Tak, MH 2011, A new stability region analysis of continuous-time Takagi-Sugeno fuzzy systems using fuzzy Lyapunov functions. in ICCAS 2011 - 2011 11th International Conference on Control, Automation and Systems., 6106260, pp. 1652-1655, 2011 11th International Conference on Control, Automation and Systems, ICCAS 2011, Gyeonggi-do, Korea, Republic of, 11/10/26.

A new stability region analysis of continuous-time Takagi-Sugeno fuzzy systems using fuzzy Lyapunov functions. / Lee, Dong Hwan; Park, Jin Bae; Joo, Young Hoon; Tak, Myung Hwan.

ICCAS 2011 - 2011 11th International Conference on Control, Automation and Systems. 2011. p. 1652-1655 6106260.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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N2 - In this paper, we propose a new sufficient condition in the form of eigenvalue problem (EVP) for assessing the stability of continuous-time Takagi-Sugeno (T-S) fuzzy systems and estimating the domain of attraction (DA) based on fuzzy Lyapunov functions (FLFs). In order to deal with the time-derivatives of the fuzzy weighting functions (TDFWFs) in the Lyapunov inequality, the existing conditions consider the upper bound on each TDFWF's absolute value. The main result of this paper is derived considering an inequality constraint of a nonlinear function depending quadratically on the fuzzy weighting functions. Finally, an example is given to demonstrate the effectiveness and validity of the proposed approach.

AB - In this paper, we propose a new sufficient condition in the form of eigenvalue problem (EVP) for assessing the stability of continuous-time Takagi-Sugeno (T-S) fuzzy systems and estimating the domain of attraction (DA) based on fuzzy Lyapunov functions (FLFs). In order to deal with the time-derivatives of the fuzzy weighting functions (TDFWFs) in the Lyapunov inequality, the existing conditions consider the upper bound on each TDFWF's absolute value. The main result of this paper is derived considering an inequality constraint of a nonlinear function depending quadratically on the fuzzy weighting functions. Finally, an example is given to demonstrate the effectiveness and validity of the proposed approach.

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Lee DH, Park JB, Joo YH, Tak MH. A new stability region analysis of continuous-time Takagi-Sugeno fuzzy systems using fuzzy Lyapunov functions. In ICCAS 2011 - 2011 11th International Conference on Control, Automation and Systems. 2011. p. 1652-1655. 6106260