LMI-based Stability and Performance Conditions for Continuous-time Nonlinear Systems in Takagi-Sugeno's Form

This paper presents the stability analysis and performance design of the continuous-time fuzzy-model-based control systems. A nonlinear controller will be proposed to stabilize the nonlinear systems in Takagi-Sugeno's form. LMI-based stability conditions will be derived the parameter-dependent Lyapunov function to guarantee the system stability. Furthermore, based on the commonly-used performance index, LMI-based performance conditions will be derived to achieve the system performance. A numerical example will be given to illustrate the effectiveness of the proposed approach.

[1]  Marcelo C. M. Teixeira,et al.  On relaxed LMI-based designs for fuzzy regulators and fuzzy observers , 2001, 2001 European Control Conference (ECC).

[2]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

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

[4]  Wen-June Wang,et al.  Flexible stability criteria for a linguistic fuzzy dynamic system , 1999, Fuzzy Sets Syst..

[5]  Zengqi Sun,et al.  Analysis and design of fuzzy reduced-dimensional observer and fuzzy functional observer , 2001, Fuzzy Sets Syst..

[6]  Xiaodong Liu,et al.  Approaches to quadratic stability conditions and H∞ control designs for T-S fuzzy systems , 2003, IEEE Trans. Fuzzy Syst..

[7]  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..

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

[9]  Heinz Unbehauen,et al.  Structure Identification of Functional-Type Fuzzy Models with Application to Modeling Nonlinear Dynamic Plants , 1997, Fuzzy Days.

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

[11]  Kazuo Tanaka,et al.  A multiple Lyapunov function approach to stabilization of fuzzy control systems , 2003, IEEE Trans. Fuzzy Syst..

[12]  Sangchul Won,et al.  A new fuzzy Lyapunov function approach for a Takagi-Sugeno fuzzy control system design , 2006, Fuzzy Sets Syst..

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

[14]  Peng Yang,et al.  Further studies on LMI-based relaxed stabilization conditions for nonlinear systems in Takagi-Sugeno's form , 2006, Autom..

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

[16]  Thierry-Marie Guerra,et al.  LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form , 2004, Autom..

[17]  Karl-Erik Årzén,et al.  Piecewise quadratic stability of fuzzy systems , 1999, IEEE Trans. Fuzzy Syst..

[18]  Chieh-Li Chen,et al.  Analysis and design of fuzzy control system , 1993 .