DOI QR코드

DOI QR Code

Nonquadratic Stability Condition of Continuous Fuzzy Systems

  • Kim, Eun-Tai (Dept. of Electrical and Electronic Engr., Yonsei University) ;
  • Park, Min-Kee (Dept. of Electronic and Information Engr., Seoul National University of Technology)
  • Published : 2003.10.01

Abstract

In this paper, a new asymptotic stability condition of continuous fuzzy system is proposed. The new stability condition considers the nonquadratic stability by using the P-matrix measure. Later the relationship of the suggested stability condition and the well-known stability condition is discussed and it is shown in a rigorous manner that the proposed criterion includes the conventional conditions.

Keywords

References

  1. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control," IEEE Trans. Systems Man Cybernet, vol. 15, No. 1 , pp116-132, 1985
  2. E. Kim and H. Lee, "New approaches to relaxed quadratic stability condition of fuzzy control systems," IEEE Trans. Fuzzy Systems, vol. 8, No. 5, pp 523-534, Oct., 2000. https://doi.org/10.1109/91.873576
  3. K. Tanaka, A Theory of Advanced Fuzzy Control, Japan:Kyuoritsu Pub, 1994. (In Japanese)
  4. K. S. Narendra and J. Balakrishnan, "A common Lyapunov for stable LTI systems with commuting A-matrices," IEEE Trans. Automat. Contr., vol. 39, pp. 2469-2471, Dec. 1994. https://doi.org/10.1109/9.362846
  5. H. O. Wang, K. Tanaka, M. F. Griffin, "An approach to fuzzy control of nonlinear systems: stability and design issues," IEEE Trans. Fuzzy Systems, vol. 4, No. 1, pp 14-23, Feb 1996. https://doi.org/10.1109/91.481841
  6. X. Ma, Z. Sun, and Y. He, "Analysis and design of fuzzy controller and fuzzy observer," IEEE Trans. Fuzzy Systems, vol. 6, No. 1, pp 41-51, Feb., 1998. https://doi.org/10.1109/91.660807
  7. C. S. Teng, B. S. Chen and H. J. Uang, "Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model," IEEE Trans. Fuzzy Systems, vol. 9, no. 3, pp 381-393, Jun. 2001. https://doi.org/10.1109/91.928735
  8. Y. - Y. Cao and Z. Lin, "Robust stability analysis and fuzzy-scheduling control for nonlinear systems subject to actuator saturation," IEEE Trans. on Fuzzy Systems, pp 57- 67, vol. 11, no. 1, 2003. https://doi.org/10.1109/TFUZZ.2002.806317
  9. M. Vidyasagar, Nonlinear Systems Analysis, Englewood Cliffs, NJ: Prentice-Hall, 1993.
  10. M A. L. Thathachar and P. Viswanath, "On the stability of fuzzy systems," IEEE Trans. Fuzzy Systems, vol. 5, No. 1, pp 145-151, Feb 1997. https://doi.org/10.1109/91.554461