An LMI approach to robust controller designs of Takagi-Sugeno fuzzy systems with parametric uncertainties

This paper proposes a new robust stability condition for Takagi-Sugeno (T-S) fuzzy control system with parametric uncertainties. The condition is represented in the form of linear matrix inequalities (LMIs) and is less conservative than some relaxed quadratic stabilization conditions published recently in the literature by collecting the interrelations of fuzzy subsystems into a set of matrices, not just into a single matrix. Based on the LMI-based conditions derived, one can easily synthesize controllers for state feedback robust stabilization for T-S fuzzy control system with parametric uncertainties. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. Finally, the validity of the proposed approach is successfully demonstrated in the the control of simulation table.

[1]  Shaocheng Tong,et al.  Observer-based robust fuzzy control of nonlinear systems with parametric uncertainties , 2002, Fuzzy Sets Syst..

[2]  Chun-Hsiung Fang,et al.  A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems , 2006, IEEE Trans. Fuzzy Syst..

[3]  Xiaodong Liu,et al.  New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI , 2003, Autom..

[4]  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).

[5]  Yung-Sheng Liu,et al.  A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems , 2003, SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme - System Security and Assurance (Cat. No.03CH37483).

[6]  Joongseon Joh,et al.  On the stability issues of linear Takagi-Sugeno fuzzy models , 1998, IEEE Trans. Fuzzy Syst..

[7]  A. El Hajjaji,et al.  Output robust stabilisation of uncertain Takagi-Sugeno model , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[8]  Gang Feng,et al.  H∞ control of uncertain fuzzy continuous-time systems , 2000, Fuzzy Sets Syst..

[9]  Euntai Kim,et al.  New approaches to relaxed quadratic stability condition of fuzzy control systems , 2000, IEEE Trans. Fuzzy Syst..

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

[11]  Jin Bae Park,et al.  Robust fuzzy control of nonlinear systems with parametric uncertainties , 2001, IEEE Trans. Fuzzy Syst..

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

[13]  Kiriakos Kiriakidis,et al.  Fuzzy model-based control of complex plants , 1998, IEEE Trans. Fuzzy Syst..

[14]  L. Xiaodong,et al.  New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI , 2003, Autom..

[15]  J. Ragot,et al.  State estimation of uncertain multiple model with unknown inputs , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[16]  Wen-June Wang,et al.  Relaxed stability and stabilization conditions for a T-S fuzzy discrete system , 2005, Fuzzy Sets Syst..

[17]  Ahmed El Hajjaji,et al.  Comment on "Observer-based robust fuzzy control of nonlinear systems with parametric uncertainties" , 2006, Fuzzy Sets Syst..