Improvements on Non-Quadratic Stabilization of Takagi-Sugeno Models Via Line-Integral Lyapunov Functions

Abstract This paper introduces two different generalizations on non-quadratic stabilization of Takagi-Sugeno models via line-integral Lyapunov functions. Inspired in recent developments which have proved to relax the conservativeness in the quadratic framework via suitable matrix transformations using a more general class of Lyapunov functions, the results here provided outperform the existing ones for line-integral Lyapunov functions with a linear matrix inequalities (LMI) form instead of bilinear matrix inequalities (BMI) in second order systems. Examples are provided to illustrate the advantages of the proposed technique over the existing approach.

[1]  Antonio Sala,et al.  Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya's theorem , 2007, Fuzzy Sets Syst..

[2]  Robert E. Skelton,et al.  Stability tests for constrained linear systems , 2001 .

[3]  I. Postlethwaite,et al.  Linear Matrix Inequalities in Control , 2007 .

[4]  Kazuo Tanaka,et al.  Model construction, rule reduction, and robust compensation for generalized form of Takagi-Sugeno fuzzy systems , 2001, IEEE Trans. Fuzzy Syst..

[5]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[6]  Ricardo C. L. F. Oliveira,et al.  Robust state feedback LMI methods for continuous-time linear systems: Discussions, extensions and numerical comparisons , 2011, 2011 IEEE International Symposium on Computer-Aided Control System Design (CACSD).

[7]  Pierre Apkarian,et al.  Parameterized linear matrix inequality techniques in fuzzy control system design , 2001, IEEE Trans. Fuzzy Syst..

[8]  Robert Babuska,et al.  Perspectives of fuzzy systems and control , 2005, Fuzzy Sets Syst..

[9]  Thierry-Marie Guerra,et al.  Construction of extended Lyapunov functions and control laws for discrete-time TS systems , 2012, 2012 IEEE International Conference on Fuzzy Systems.

[10]  Thierry-Marie Guerra,et al.  Generalized Nonquadratic Stability of Continuous-Time Takagi–Sugeno Models , 2010, IEEE Transactions on Fuzzy Systems.

[11]  Kevin Guelton,et al.  New controllers and new designs for continuous-time Takagi-Sugeno models , 2012, 2012 IEEE International Conference on Fuzzy Systems.

[12]  Gang Feng,et al.  Controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions and bilinear matrix inequalities , 2003, The 12th IEEE International Conference on Fuzzy Systems, 2003. FUZZ '03..

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

[14]  Kazuo Tanaka,et al.  Guaranteed cost control of polynomial fuzzy systems via a sum of squares approach , 2007, 2007 46th IEEE Conference on Decision and Control.

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

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

[17]  Miguel Bernal,et al.  A membership-function-dependent approach for stability analysis and controller synthesis of Takagi-Sugeno models , 2009, Fuzzy Sets Syst..

[18]  Kevin Guelton,et al.  Robust dynamic output feedback fuzzy Lyapunov stabilization of Takagi-Sugeno systems - A descriptor redundancy approach , 2009, Fuzzy Sets Syst..

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

[20]  P. Olver.  Nonlinear Systems , 2013 .

[21]  Dennis G. Zill,et al.  Advanced Engineering Mathematics , 2021, Technometrics.

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

[23]  Reinaldo M. Palhares,et al.  A systematic approach to improve multiple Lyapunov function stability and stabilization conditions for fuzzy systems , 2009, Inf. Sci..

[24]  Kevin Guelton,et al.  Comments on Fuzzy Control Systems Design via Fuzzy Lyapunov Functions , 2010, IEEE Trans. Syst. Man Cybern. Part B.

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

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

[27]  Gang Feng,et al.  H/sub /spl infin// controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions and bilinear matrix inequalities , 2005, IEEE Transactions on Fuzzy Systems.

[28]  Miguel Bernal,et al.  Strategies to Exploit Non-Quadratic Local Stability Analysis , 2012 .

[29]  Kazuo Tanaka,et al.  Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach , 2008 .