Observer-based controller for Takagi-Sugeno models

This paper studies the stabilisation of the T-S (Takagi-Sugeno) model using an output feedback controller. Both measurable and estimated decision variable cases are considered. In the case of measurable decision variables a T-S observer and T-S controller are designed separately to stabilise globally exponentially the closed loop T-S model. When the decision variables depend on the state variables estimated by the T-S observer, a procedure to design a stabilising output feedback controller is proposed. An example is given to illustrate the result.

[1]  Kazuo Tanaka,et al.  An approach to fuzzy control of nonlinear systems: stability and design issues , 1996, IEEE Trans. Fuzzy Syst..

[2]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[3]  Thierry-Marie Guerra,et al.  Control laws for Takagi-Sugeno fuzzy models , 2001, Fuzzy Sets Syst..

[4]  Bengt Lennartson,et al.  An LMI approach for stability analysis of nonlinear systems , 1997, 1997 European Control Conference (ECC).

[5]  Wook Hyun Kwon,et al.  Stability analysis and stabilization of fuzzy state space models , 1995 .

[6]  Wen-June Wang,et al.  Relaxed stability conditions for T-S fuzzy systems , 2001, Proceedings Joint 9th IFSA World Congress and 20th NAFIPS International Conference (Cat. No. 01TH8569).

[7]  Juan Luis Castro,et al.  Fuzzy logic controllers are universal approximators , 1995, IEEE Trans. Syst. Man Cybern..

[8]  James J. Buckley,et al.  Universal fuzzy controllers , 1992, Autom..

[9]  Akira Ichikawa,et al.  Design of output feedback controllers for Takagi-Sugeno fuzzy systems , 2001, Fuzzy Sets Syst..

[10]  Eun Tae Jeung,et al.  Observer-based fuzzy H/sup /spl infin// control for uncertain nonlinear systems with time delays , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[11]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[12]  J. Ragot,et al.  On the stability analysis of multiple model systems , 2001, 2001 European Control Conference (ECC).

[13]  GuerraThierry Marie,et al.  Control laws for TakagiSugeno fuzzy models , 2001 .

[14]  Roderick Murray-Smith,et al.  Multiple Model Approaches to Modelling and Control , 1997 .

[15]  C. J. Lopez-Toribio,et al.  Takagi-Sugeno fuzzy fault-tolerant control for a non-linear system , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[16]  José Ragot,et al.  Output stabilisation in multiple model approach to modelling , 2002, Proceedings of the International Conference on Control Applications.

[17]  Anders Rantzer,et al.  Piecewise linear quadratic optimal control , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[18]  Thomas Kailath,et al.  Linear Systems , 1980 .

[19]  K. Tanaka,et al.  Multi-objective fuzzy control of high rise/high speed elevators using LMIs , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[20]  Antonio T. Alexandridis,et al.  Design of output feedback controllers and output observers , 1999 .

[21]  On the Sugeno-type fuzzy observers , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[22]  Kazuo Tanaka,et al.  Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs , 1998, IEEE Trans. Fuzzy Syst..