Paper:

# Robust Output Feedback Guaranteed Cost Control of Uncertain Fuzzy Systems with Immeasurable Premise Variables

## Jun Yoneyama

Department of Electronics and Electrical Engineering, Aoyama Gakuin University, 5-10-1 Fuchinobe, Sagamihara, Kanagawa 229-8558, Japan

This paper is concerned with robust output feedback stabilization with guaranteed cost of uncertain Takagi-Sugeno fuzzy systems with immeasurable premise variables. When we consider Takagi-Sugeno fuzzy systems, the selection of premise variables plays an important role. If the premise variable is the state of the system, then a fuzzy system describes a wide class of nonlinear systems. However, the state is not measurable in the output feedback control problem. In this case, a control design based on parallel distributed compensation is impossible because a controller depends on immeasurable premise variables. In this paper, we consider the robust output feedback stabilization problem with guaranteed cost where the premise variable is not measurable. We formulate this problem as a robust stabilization of uncertain linear systems. Numerical examples are given to illustrate our theory.

*J. Adv. Comput. Intell. Intell. Inform.*, Vol.11, No.7, pp. 745-750, 2007.

- [1] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, “Linear Matrix Inequalities in Systems and Control Theory,” SIAM, 1994.
- [2] G. Feng, S. G. Gao, N. W. Rees, and C. K. Chak, “Design of fuzzy control systems with guaranteed stability,” Fuzzy Sets and Systems, Vol.85, pp. 1-10, 1997.
- [3] S. W. Kau, H. J. Lee, C. M. Yang, C. H. Lee, L. Hong, and C. H. Fang, “Robust H
_{∞}fuzzy static output feedback control of T-S fuzzy systems with parametric uncertainties,” Fuzzy Sets and Systems, Vol.158, pp. 135-146, 2007. - [4] T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Transaction on Systems, Man, Cybernetics, Vol.15, pp. 116-132, 1985.
- [5] K. Tanaka, T. Ikeda, and H. O. Wang, “Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability,
*H*^{∞}control theory, and linear matrix inequalities,” IEEE Transaction on Fuzzy Systems, Vol.4, pp. 1-13, 1996. - [6] K. Tanaka and H. O. Wang, “Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach,” Wiley-Interscience, 2001.
- [7] K. Tanaka and M. Sano, “On the concepts of regulator and observer of fuzzy control systems,” 3rd IEEE International Conference on Fuzzy Systems, pp. 767-772, 1994.
- [8] K. Tanaka and M. Sugeno, “Stability analysis and design of fuzzy control systems,” Fuzzy Sets and Systems, Vol.45, pp. 135-156, 1992.
- [9] H. D. Tuan, P. Apkarian, T. Narikiyo, and M. Kanota, “New fuzzy control model and dynamic output feedback parallel distributed compensation,” IEEE Transaction on Fuzzy Systems, Vol.12, pp. 13-21, 2004.
- [10] L. Xie, “Output feedback H
_{∞}control of systems with parameter uncertainty,” International Journal of Control, Vol.63, pp. 741-759, 1996. - [11] J. Yoneyama, “Output stabilization of Takagi-Sugeno fuzzy systems with unobservable premise variables,” IEEE International Conference on System of Systems Engineering, pp. 65-70, 2006.
- [12] J. Yoneyama, “H
_{∞}output feedback control of fuzzy systems with immeasurable premise variables,” IEEE International Conference on Information Reuse and Integration, pp. 454-459, 2006. - [13] J. Yoneyama, M. Nishikawa, H. Katayama, and A. Ichikawa, “Design of output feedback controllers for Takagi-Sugeno fuzzy systems,” Fuzzy Sets and Systems, Vol.121, pp. 127-148, 2001.