Stabilization of positive constrained T-S fuzzy systems: Application to a Buck converter

Abstract This paper deals with the problem of constrained stability and tracking of Takagi–Sugeno (T–S) fuzzy positive systems. Linear programming (LP) is used to insert the constraints in the design phase while imposing positivity in closed-loop. The theoretical results are applied to the buck DC–DC converter which is widely used in the photovoltaic generators. Based on the simulation results success of the method is shown for this application.

[1]  Ahmed El Hajjaji,et al.  DELAY-DEPENDENT STABILIZATION CONDITIONS OF CONTROLLED POSITIVE TS FUZZY SYSTEMS WITH TIME VARYING DELAY , 2011 .

[2]  Chien-Yu Huang,et al.  LMI-based Integral fuzzy control of DC-DC converters , 2006, IEEE Transactions on Fuzzy Systems.

[3]  Tadeusz Kaczorek,et al.  Stability of positive continuous-time linear systems with delays , 2009, 2009 European Control Conference (ECC).

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

[5]  Tingshu Hu,et al.  An analysis and design method for linear systems subject to actuator saturation and disturbance , 2002, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[6]  Abdellah Benzaouia,et al.  Regulator problem for linear systems with constraints on control and its increment or rate , 2004, Autom..

[7]  Barbara Zitov a.  Journal of the Franklin Institute , 1942, Nature.

[8]  Abdellah Benzaouia,et al.  Stability and stabilization by output feedback control of positive Takagi–Sugeno fuzzy discrete-time systems with multiple delays , 2014 .

[9]  A. Hmamed,et al.  Stabilization of controlled positive discrete‐time T‐S fuzzy systems by state feedback control , 2010 .

[10]  Abdellah Benzaouia.  Saturated Switching Systems , 2012 .

[11]  Jérôme Bosche,et al.  Robust output tracking control of T-S fuzzy systems and its application to DC-DC converters , 2011 .

[12]  L X Wang,et al.  Fuzzy basis functions, universal approximation, and orthogonal least-squares learning , 1992, IEEE Trans. Neural Networks.

[13]  Yoshito Ohta.  Positive linear systems: theory and applications: Lorenzo Farina and Sergio Rinaldi; John Wiley, New York, 2000, ISBN 0-471-38456-9 , 2003, Autom..

[14]  Zhicheng Ji,et al.  T-S modeling, Simulation and Control of the Buck Converter , 2008, 2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery.

[15]  Abdellah Benzaouia,et al.  Memoryless Control to Drive States of Delayed Continuous-time Systems within the Nonnegative Orthant , 2008 .

[16]  Ahmed El Hajjaji,et al.  Stabilization of positive Takagi-Sugeno fuzzy discrete-time systems with multiple delays and bounded controls , 2014, J. Frankl. Inst..

[17]  Jon Rigelsford,et al.  Positive 1D and 2D Systems , 2002 .

[18]  Abdelhamid Rabhi,et al.  Integral Fuzzy Control for Photovoltaic Power Systems , 2009 .

[19]  Abdellah Benzaouia,et al.  The Regulator Problem for Linear Systems With Saturations on the Control and its Increments or Rate: An LMI Approach , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.