STABILITY OF TAKAGI-SUGENO FUZZY SYSTEMS

İlker Üstoğlu

Abstract

Takagi-Sugeno (T-S) fuzzy models are usually used to describe nonlinear systems by a set of IF-THEN rules that gives local linear representations of subsystems. The overall model of the system is then formed as a fuzzy blending of these subsystems. It is important to study their stability or the synthesis of stabilizing controllers. The stability of TS models has been derived by means of several methods: Lyapunov approach, switching systems theory, linear system with modeling uncertainties, etc. In this study, the uniform stability, and uniform exponential stability of a discrete time T-S model is examined. Moreover, a perturbation result and an instability condition are given. The subsystems of T-S models that is studied here are time varying and a new exponential stability theorem is given for these types of TS models by examining the existence of a common matrix sequence.

References

  1. Boyd, S., 1994. et al. Linear matrix inequalities in systems and control theory. Philadelphia, PA, SIAM.
  2. Calcev, G., 1998. “Some remarks on the stability of Mamdani fuzzy control systems”, IEEE Trans. Fuzzy Syst., 6(3), 436-442
  3. Jamshidi, M., 1997. Large Scale Systems. Prentice Hall.
  4. Kim, E., Kim, D., 2001. “Stability analysis and synthesis for an affine fuzzy systems via LMI and ILMI: discrete case”, IEEE Trans. Syst. Man Cybern. B. Cybern., 31(1), 132-140
  5. Takagi, T., Sugeno, M., 1985. “Fuzzy identification of systems and its applications to modeling and control”, IEEE Trans. on Systems, Man, and Cybernetics, vol.15(1), 116-132.
  6. Tanaka, K., Sugeno, M., 1990. Stability analysis of fuzzy systems using Lyapunov's direct method, Proc. of NAFIPS'90, 133-136.
  7. Tanaka, K., Sugeno, M., 1992. “Stability analysis and design of fuzzy control systems”, Fuzzy Sets Systems, vol.45(2), 135-156.
  8. Tanaka, K., Ikeda, T., Wang, H. O., 1996. “Quadratic Stability and Stabilization of Fuzzy Control Systems”. Fuzzy Information Processing Society. NAFIPS.
  9. Rugh, W. J., 1996. Linear System Theory, 2nd ed., Prentice Hall.
  10. Wang, L.-X., 1996. A Course in Fuzzy Systems and Control, Prentice Hall.
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Paper Citation


in Harvard Style

Üstoğlu İ. (2006). STABILITY OF TAKAGI-SUGENO 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 213-216. DOI: 10.5220/0001214802130216


in Bibtex Style

@conference{icinco06,
author={İlker Üstoğlu},
title={STABILITY OF TAKAGI-SUGENO FUZZY SYSTEMS},
booktitle={Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2006},
pages={213-216},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001214802130216},
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 - STABILITY OF TAKAGI-SUGENO FUZZY SYSTEMS
SN - 978-972-8865-59-7
AU - Üstoğlu İ.
PY - 2006
SP - 213
EP - 216
DO - 10.5220/0001214802130216