Robust Fuzzy Observer Design for Nonlinear Systems

This paper shows a new method for design of fuzzy observers for Takagi-Sugeno systems. The method is based on Linear matrix inequalities (LMIs) and it allows to insert H constraint into the design procedure. The speed of estimation can tuned be specification of a decay rate of the observer closed loop system. We discuss here also the influence of parametric uncertainties at the output control system stability.

• Michal Polanský
• C. Ardil

• H norm
• Linear Matrix Inequalities
• Observers
• Takagi-Sugeno Systems
• Parallel Distributed Compensation

[1] K. R. Lee, E. T. Jeung, H. B. Park, "Robust fuzzy H control for
uncertain nonlinear systems via state feedback: an LMI approach".
Fuzzy Sets and Systems. 2001, vol. 120, p. 123-134
[2] M. Polansky, "Nová metoda ARPDC pro zvÛšení kvality robustního
r├¡zen├¡ neline├írn├¡ch systému" Dissertation thesis, Faculty of electrical
engineering and Communication at Brno University of Technology,
2005, in Czech
[3] X. J. Ma, Z. Q. Sun, "Analysis and design of fuzzy controller and fuzzy
observer" IEEE Trans. Fuzzy Systems. 1998, vol. 6, no. 1, p. 41-51.
[4] T. Takagi, M. Sugeno, "Fuzzy identification of systems and its
applications to modeling and control" IEEE Transactions on Systems,
Man and Cybernetics. 1985, vol. 1, no. 1, p. 116-132
[5] S. Boyd, L. El Ghaoui, E. Ieron, V. Balakrishnan, "Studies in Applied
Mathematics : Linear Matrix Inequalities in System and
ControlTheory". SIAM, Philadelphia, PA, 1994
[6] S.G.Cao, N.W.Rees, G. Feng, H control of uncertain fuzzy continuoustime
systems. Fuzzy Sets and Systems. 2000, vol. 115, p. 171-190
[7] V. Kucera, Analysis and design of discrete linear control systems.
Prentice Hall, 1991