Stabilization of discrete-time 2D T-S fuzzy systems by state feedback control

This paper deals with sufficient conditions of asymptotic stability for non linear discrete-time 2D systems represented by a Takagi-Sugeno fuzzy model of Roesser type with state feedback control. This work is based on common and multiple Lyapunov functions. The results are presented in LMI's form.

[1]  Donald D. Givone,et al.  Multidimensional Linear Iterative Circuits - General Properties , 1972, IEEE Trans. Computers.

[2]  R. Roesser.  A discrete state-space model for linear image processing , 1975 .

[3]  G. Marchesini,et al.  State-space realization theory of two-dimensional filters , 1976 .

[4]  W. Marszalek.  Two-dimensional state-space discrete models for hyperbolic partial differential equations , 1984 .

[5]  W.-s. Lu,et al.  Comments on "Stability for Two-Dimensional Systems via a Lyapunov Approach , 1985 .

[6]  Engin Yaz,et al.  On state-feedback stabilization of two-dimensional digital systems , 1985 .

[7]  E. B. Lee,et al.  Stabilization of two-dimensional systems , 1985 .

[8]  Wu-Sheng Lu,et al.  Comments on stability analysis for two-dimensional systems via a Lyapunov approach , 1985 .

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

[10]  Brian D. O. Anderson,et al.  Stability and the matrix Lyapunov equation for discrete 2-dimensional systems , 1986 .

[11]  Wu-Sheng Lu,et al.  Some new results on stability robustness of two-dimensional discrete systems , 1994, Multidimens. Syst. Signal Process..

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

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

[14]  Mohammed Chadli,et al.  An LMI formulation for output feedback stabilization in multiple model approach , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[15]  Shengyuan Xu,et al.  LMIs - a fundamental tool in analysis and controller design for discrete linear repetitive processes , 2002 .

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

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

[18]  Gang Feng,et al.  Stability analysis of discrete-time fuzzy dynamic systems based on piecewise Lyapunov functions , 2004, IEEE Trans. Fuzzy Syst..

[19]  Ahmed El Hajjaji,et al.  Four wheel steering control by fuzzy approach , 2005, J. Intell. Robotic Syst..

[20]  Ettore Fornasini,et al.  Doubly-indexed dynamical systems: State-space models and structural properties , 1978, Mathematical systems theory.

[21]  Abdellah Benzaouia,et al.  LMI-based approach for output-feedback stabilization for discrete time Takagi-Sugeno systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[22]  A. Benzaouia,et al.  Stabilization of fuzzy systems with constrained controls by using positively invariant sets , 2006 .

[23]  Abdellah Benzaouia,et al.  Static output-feedback stabilization for time-delay Takagi-Sugeno fuzzy systems , 2007, 2007 46th IEEE Conference on Decision and Control.

[24]  Ahmed El Hajjaji,et al.  Piecewise quadratic Lyapunov function for nonlinear systems with fuzzy static output feedback control , 2007, 2007 European Control Conference (ECC).

[25]  Mohammed Alfidi,et al.  LMI Conditions for Robust Stability of 2D Linear Discrete-Time Systems , 2008 .