Stability analysis of a class of MIMO fuzzy control systems

This paper suggests a new stability analysis approach dedicated to a class of fuzzy control systems controlling multi input-multi output (MIMO) nonlinear processes by means of Takagi-Sugeno fuzzy logic controllers. The approach is based on LaSalle's global invariant set theorem, and an original stability theorem offers sufficient stability conditions. The applicability and efficiency of the theoretical results are illustrated by a MIMO case study dealing with the fuzzy control of a spherical three tank system.

[1]  Trevor P. Martin,et al.  Fuzzy sets in the fight against digital obesity , 2005, Fuzzy Sets Syst..

[2]  Chunyu Yang,et al.  Multiobjective Control for T–S Fuzzy Singularly Perturbed Systems , 2009, IEEE Transactions on Fuzzy Systems.

[3]  Piero P. Bonissone,et al.  Multicriteria decision making (mcdm): a framework for research and applications , 2009, IEEE Computational Intelligence Magazine.

[4]  Markus Reischl,et al.  Takagi--Sugeno--Kang Fuzzy Classifiers for a Special Class of Time-Varying Systems , 2008, IEEE Transactions on Fuzzy Systems.

[5]  Zdenko Kovacic,et al.  Time Windows Based Dynamic Routing in Multi-AGV Systems , 2010, IEEE Transactions on Automation Science and Engineering.

[6]  Hak-Keung Lam,et al.  Stability Analysis and Performance Design for Fuzzy-Model-Based Control System Under Imperfect Premise Matching , 2009, IEEE Transactions on Fuzzy Systems.

[7]  József K. Tar,et al.  Fuzzy Control System Performance Enhancement by Iterative Learning Control , 2008, IEEE Transactions on Industrial Electronics.

[8]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[9]  Fernando de Oliveira Souza,et al.  On Stability and Stabilization of T–S Fuzzy Time-Delayed Systems , 2009, IEEE Transactions on Fuzzy Systems.

[10]  Fernando A. C. Gomide,et al.  Hybrid neurofuzzy computing with nullneurons , 2008, 2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence).

[11]  Bernadette Bouchon-Meunier,et al.  Interpretable decisions by means of similarities and modifiers , 2009, 2009 IEEE International Conference on Fuzzy Systems.

[12]  S. Preitl,et al.  Design and Experiments for a Class of Fuzzy Controlled Servo Systems , 2008, IEEE/ASME Transactions on Mechatronics.

[13]  Masahiro Inuiguchi,et al.  A decomposition method for optimal firing sequence problems for first-order hybrid Petri nets , 2009, 2009 IEEE International Conference on Systems, Man and Cybernetics.

[14]  James M. Keller,et al.  Modeling Human Activity From Voxel Person Using Fuzzy Logic , 2009, IEEE Transactions on Fuzzy Systems.

[15]  Bart De Schutter,et al.  Stability of Cascaded Fuzzy Systems and Observers , 2009, IEEE Transactions on Fuzzy Systems.

[16]  吉澤 太郎.  An Invariance Principle in the Theory of Stability (常微分方程式及び函数微分方程式研究会報告集) , 1968 .

[17]  Rudolf Kruse,et al.  A Treatment Outcome Prediction Model of Visual Field Recovery Using Self-Organizing Maps , 2009, IEEE Transactions on Biomedical Engineering.

[18]  Gang Feng,et al.  Rapid Load Following of an SOFC Power System via Stable Fuzzy Predictive Tracking Controller , 2009, IEEE Transactions on Fuzzy Systems.

[19]  Tamer Basar.  An Invariance Principle in the Theory of Stability , 2001 .

[20]  Kazuo Tanaka,et al.  A Sum-of-Squares Approach to Modeling and Control of Nonlinear Dynamical Systems With Polynomial Fuzzy Systems , 2009, IEEE Transactions on Fuzzy Systems.

[21]  Antonio Sala,et al.  Polynomial Fuzzy Models for Nonlinear Control: A Taylor Series Approach , 2009, IEEE Transactions on Fuzzy Systems.

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

[23]  Ricardo C. L. F. Oliveira,et al.  Convergent LMI Relaxations for Quadratic Stabilizability and ${{\mathscr H}}_{\infty}$ Control of Takagi–Sugeno Fuzzy Systems , 2009, IEEE Transactions on Fuzzy Systems.