DETERMINING ELLIPSOIDAL BASINS OF ATTRACTION OF FUZZY SYSTEMS

Carlos Ariño, Antonio Sala

2006

Abstract

This paper discusses how to obtain local stability results from a fuzzy system for which global ones cannot be obtained, basically due to infeasibility of some associated LMI problems. Two different approaches are compared: modifying the consequent models vs. setting up some relaxed LMI conditions if bounds on the memberships are known. Some examples are used to illustrate the approaches.

References

  1. Boyd, S., ElGhaoui, L., Feron, E., and Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory. Ed. SIAM, Philadelphia, USA.
  2. Johansson, M. (1999). Piecewise quadratic stability of fuzzy systems. IEEE Trans. Fuzzy Syst., 7:713-722.
  3. Khalil, H. (1996). Nonlinear Systems (2nd. ed.). Ed. Prentice-Hall, Upper Saddle River, New Jersey, USA.
  4. Luenberger, D. (2003). Linear and Nonlinear Programming. Springer, 2nd edition.
  5. Oliveira, M. d., Bernussou, J., and Geromel, J. (1999). Anew discrete-time robust stability condition. System & Control Letters, 37:261-265.
  6. Takagi, T. and Sugeno, M. (1985). Fuzzy identification of systems and its applications to modelling and control. IEEE Trans. on Systems, Man and Cybernetics, 15(1):116-132.
  7. Tanaka, K. and Wang, H. O. (2001). Fuzzy control systems design and analysis. Ed. John Wiley & Sons, New York, USA.
  8. Wang, H. O., Tanaka, K., and Griffin, M. F. (1996). An approach to fuzzy control of nonlinear systems: Stability and design issues. IEEE Transactions on Fuzzy Systems, 4:14-23.
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Paper Citation


in Harvard Style

Ariño C. and Sala A. (2006). DETERMINING ELLIPSOIDAL BASINS OF ATTRACTION OF FUZZY SYSTEMS . In Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-972-8865-59-7, pages 86-91. DOI: 10.5220/0001203200860091


in Bibtex Style

@conference{icinco06,
author={Carlos Ariño and Antonio Sala},
title={DETERMINING ELLIPSOIDAL BASINS OF ATTRACTION OF FUZZY SYSTEMS},
booktitle={Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2006},
pages={86-91},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001203200860091},
isbn={978-972-8865-59-7},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - DETERMINING ELLIPSOIDAL BASINS OF ATTRACTION OF FUZZY SYSTEMS
SN - 978-972-8865-59-7
AU - Ariño C.
AU - Sala A.
PY - 2006
SP - 86
EP - 91
DO - 10.5220/0001203200860091