Stability Analysis of TSK Fuzzy Systems

TSK퍼지 시스템의 안정도 해석

  • 강근택 (부경대학교 공과대학 전자공학과) ;
  • 이원창 (부경대학교 공과대학 전자공학과)
  • Published : 1998.08.01

Abstract

This paper describes the stability analysis of TSK (Takagi-Sugeno-Kang) fuzzy systems which can represent a large class of nonlinear systems with good accuracy. A TSK fuzzy model consists of TSK fuzzy rules and the consequent of each fuzzy rule is a linear input-output equation with a constant term. There may exist equilibrium points more than one in the TSK fuzzy model and each equilibrium point rnay also have different nature of stability. The local stability of an equilibrium point is determined by eigenvalues of the Jacobian matrix of the linearized TSK fuzzy model around the equilibrium point. Stability of both the continuous-time and the discrete-time systems is analyzed in this paper.

본 논문에서는 넓은 범위의 비선형 시스템들을 잘 표현할 수 있는 TSK(Takagai Sugeno Kang) 퍼지 시스템의 평형점의 지역 안정도를 해석하는 방법을 제시한다. TSK퍼지 모델은 TSK퍼지 규칙들로 구성되며, 각 규칙의 결론부는 상수항을 갖는 선형 입출력 방정식이다. TSK퍼지모델은 다수의평형점을 가질수 있으며, 각 평형점은 안정도에 있어서 역시 서로 단른 특징을 가질수 있다. 평형점의 지역 안정도는 평형점 부근에서 TSK퍼지 모델의 선형화로 얻어지는 자코비안 행렬의 교유치에 의해 결정된다. 본 논문에서는 연속시간 및 이산시간 시스템에 대한 안정도 해석을 위한 방법이 각각 제시된다.

Keywords

References

  1. IEEE Trans. on SMC v.15 no.1 Fuzzy Identification of Systems and Its Applications to Modelling and Control T.Takagi;M.Sugeno
  2. Fuzzy Sets and Systems v.28 Structure Identification of Fuzzy Model M.Sugeno;G.Kang
  3. Fuzzy Sets and Systems v.53 Sugeno type controllers are universal controller J.Buckley
  4. Fuzzy Sets and Systems v.16 Fuzzy Control of Model Car M.Sugeno;M.Nishida
  5. Fuzzy Sets and Systems v.18 Fuzzy Modelling and Control of Multilayer Incinerator M.Sugeno;G.Kang
  6. Proc. International Fuzzy Systems Association World Congress Hull Form Generation by Using Fuzzy Model Y.S.Lee;S.J.Jeong;S.Y.Kim;G.Kang
  7. Proc. International Fuzzy Systems Association World Congress Design of Fuzzy Controller Based on Fuzzy Model for Container crane System M.Kim;G.Kang
  8. Fuzzy Sets and Systems v.45 Stability Analysis and Design of Fuzzy Control Systems K.Tanaka;M.Sugeno
  9. Proc. IEEE International Conference on Fuzzy Systems On the Concepts of Regulator and Observer of Fuzzy Control System K.Tanaka;M.Sano
  10. Proc. International Fuzzy Systems Association World Congress Design of Fuzzy Parameter Adaptive Controllers G.Kang;W.Lee
  11. Proc. IEEE International Conference on Fuzzy Systems Application of Implicit Self-Tuning Fuzzy control to Nonlinear Systems K.Kiriakidis;A.Tzes
  12. Proc. IEEE International Conference on Fuzzy Systems Design of Fuzzy State Controllers and Observers G.Kang;W.Lee
  13. IEEE Trans. on Fuzzy Systems v.4 An Approach to Fuzzy Control of Nonlinear Systems: Stability and Design Issues H.O.Wang;K.Tanaka;M.F.Griffin
  14. IEEE Trans. on Neural Networks v.4 Identification and Control Dynamical Systems Using Neural Networks K.S.Narendra;K.Parthasarathy