Relaxed stability condition for polynomial fuzzy system: Non-quadratic Lyapunov function approach

Han Sol Kim, Jin Bae Park, Young Hoon Joo

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

1 Citation (Scopus)

Abstract

In this paper, relaxed stability of polynomial fuzzy system is considered. Proposed relaxed stability condition is based on the non-quadratic Lyapunov function (NQLF). Since the condition that contains the time derivative of the fuzzy weighting function (FWF) cannot be casted into linear matrix inequality (LMI) condition, various researches arbitrarily set the bound of its magnitude. To solve this problem, in this paper, the stability condition is directly calculated without setting the bound of magnitude of the time derivative of the FWF, and the condition is casted into sum-of-square (SOS) condition. Finally, to prove the superiority of proposed method, simulation example is given.

Original languageEnglish
Title of host publicationICCAS 2013 - 2013 13th International Conference on Control, Automation and Systems
Pages673-676
Number of pages4
DOIs
Publication statusPublished - 2013 Dec 1
Event2013 13th International Conference on Control, Automation and Systems, ICCAS 2013 - Gwangju, Korea, Republic of
Duration: 2013 Oct 202013 Oct 23

Other

Other2013 13th International Conference on Control, Automation and Systems, ICCAS 2013
CountryKorea, Republic of
CityGwangju
Period13/10/2013/10/23

Fingerprint

Fuzzy systems
Lyapunov functions
Polynomials
Derivatives
Linear matrix inequalities

All Science Journal Classification (ASJC) codes

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

Cite this

Kim, H. S., Park, J. B., & Joo, Y. H. (2013). Relaxed stability condition for polynomial fuzzy system: Non-quadratic Lyapunov function approach. In ICCAS 2013 - 2013 13th International Conference on Control, Automation and Systems (pp. 673-676). [6703954] https://doi.org/10.1109/ICCAS.2013.6703954
Kim, Han Sol ; Park, Jin Bae ; Joo, Young Hoon. / Relaxed stability condition for polynomial fuzzy system : Non-quadratic Lyapunov function approach. ICCAS 2013 - 2013 13th International Conference on Control, Automation and Systems. 2013. pp. 673-676
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Kim, HS, Park, JB & Joo, YH 2013, Relaxed stability condition for polynomial fuzzy system: Non-quadratic Lyapunov function approach. in ICCAS 2013 - 2013 13th International Conference on Control, Automation and Systems., 6703954, pp. 673-676, 2013 13th International Conference on Control, Automation and Systems, ICCAS 2013, Gwangju, Korea, Republic of, 13/10/20. https://doi.org/10.1109/ICCAS.2013.6703954

Relaxed stability condition for polynomial fuzzy system : Non-quadratic Lyapunov function approach. / Kim, Han Sol; Park, Jin Bae; Joo, Young Hoon.

ICCAS 2013 - 2013 13th International Conference on Control, Automation and Systems. 2013. p. 673-676 6703954.

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

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T1 - Relaxed stability condition for polynomial fuzzy system

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N2 - In this paper, relaxed stability of polynomial fuzzy system is considered. Proposed relaxed stability condition is based on the non-quadratic Lyapunov function (NQLF). Since the condition that contains the time derivative of the fuzzy weighting function (FWF) cannot be casted into linear matrix inequality (LMI) condition, various researches arbitrarily set the bound of its magnitude. To solve this problem, in this paper, the stability condition is directly calculated without setting the bound of magnitude of the time derivative of the FWF, and the condition is casted into sum-of-square (SOS) condition. Finally, to prove the superiority of proposed method, simulation example is given.

AB - In this paper, relaxed stability of polynomial fuzzy system is considered. Proposed relaxed stability condition is based on the non-quadratic Lyapunov function (NQLF). Since the condition that contains the time derivative of the fuzzy weighting function (FWF) cannot be casted into linear matrix inequality (LMI) condition, various researches arbitrarily set the bound of its magnitude. To solve this problem, in this paper, the stability condition is directly calculated without setting the bound of magnitude of the time derivative of the FWF, and the condition is casted into sum-of-square (SOS) condition. Finally, to prove the superiority of proposed method, simulation example is given.

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Kim HS, Park JB, Joo YH. Relaxed stability condition for polynomial fuzzy system: Non-quadratic Lyapunov function approach. In ICCAS 2013 - 2013 13th International Conference on Control, Automation and Systems. 2013. p. 673-676. 6703954 https://doi.org/10.1109/ICCAS.2013.6703954