Polytopic invariant and contractive sets for closed-loop discrete fuzzy systems

This work has been supported by Projects DPI2011-27845-C02-01 and DPI2011-27845-C02-02, both from Spanish Government.

[1]  Antonio Sala,et al.  On the conservativeness of fuzzy and fuzzy-polynomial control of nonlinear systems , 2009, Annu. Rev. Control..

[2]  Franco Blanchini,et al.  Set invariance in control , 1999, Autom..

[3]  B. Reznick,et al.  A new bound for Pólya's Theorem with applications to polynomials positive on polyhedra , 2001 .

[4]  Antonio Sala,et al.  Design of Multiple-Parameterisation PDC Controllers via Relaxed Conditions for Multi-Dimensional Fuzzy Summations , 2007, 2007 IEEE International Fuzzy Systems Conference.

[5]  E. Kerrigan.  Robust Constraint Satisfaction: Invariant Sets and Predictive Control , 2000 .

[6]  Antonio Sala,et al.  Relaxed Stability and Performance Conditions for Takagi–Sugeno Fuzzy Systems With Knowledge on Membership Function Overlap , 2007, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[7]  Alberto Bemporad,et al.  Stabilizing Model Predictive Control of Hybrid Systems , 2006, IEEE Transactions on Automatic Control.

[8]  K. T. Tan,et al.  Linear systems with state and control constraints: the theory and application of maximal output admissible sets , 1991 .

[9]  T. Hu,et al.  Non-conservative matrix inequality conditions for stability/stabilizability of linear differential inclusions , 2010, Autom..

[10]  Amir H. D. Markazi,et al.  Performance-oriented parallel distributed compensation , 2011, J. Frankl. Inst..

[11]  Shao-Yuan Li,et al.  Stabilization via extended nonquadratic boundedness for constrained nonlinear systems in Takagi-Sugeno's form , 2011, J. Frankl. Inst..

[12]  Kazuo Tanaka,et al.  A fuzzy Lyapunov approach to fuzzy control system design , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

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

[14]  Franco Blanchini,et al.  Ultimate boundedness control for uncertain discrete-time systems via set-induced Lyapunov functions , 1991, [1991] Proceedings of the 30th 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]  Baocang Ding,et al.  Homogeneous Polynomially Nonquadratic Stabilization of Discrete-Time Takagi–Sugeno Systems via Nonparallel Distributed Compensation Law , 2010, IEEE Transactions on Fuzzy Systems.

[17]  Eduardo F. Camacho,et al.  Constrained Model Predictive Control , 2007 .

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

[19]  Mato Baotic,et al.  Multi-Parametric Toolbox (MPT) , 2004, HSCC.

[20]  David Q. Mayne,et al.  Optimized robust control invariance for linear discrete-time systems: Theoretical foundations , 2007, Autom..

[21]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[22]  TanakaK.,et al.  Robust stabilization of a class of uncertain nonlinear systems via fuzzy control , 1996 .

[23]  Antonio Sala,et al.  A Triangulation Approach to Asymptotically Exact Conditions for Fuzzy Summations , 2009, IEEE Transactions on Fuzzy Systems.

[24]  Carlos Ariño,et al.  Maximal closed loop admissible set for linear systems with non-convex polyhedral constraints , 2011 .

[25]  V. RakovićS.,et al.  Optimized robust control invariance for linear discrete-time systems , 2007 .

[26]  Kazuo Tanaka,et al.  Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, H∞ control theory, and linear matrix inequalities , 1996, IEEE Trans. Fuzzy Syst..

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

[28]  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..

[29]  M. Sami Fadali,et al.  TSK Fuzzy Function Approximators: Design and Accuracy Analysis , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[30]  J. Suykens,et al.  The efficient computation of polyhedral invariant sets for linear systems with polytopic uncertainty , 2005, Proceedings of the 2005, American Control Conference, 2005..