New Discrete Tanaka Sugeno Kang Fuzzy Systems Characterization and Stability Domain



In this paper, an analytical approach to characterize discrete Tanaka Sugeno Kang (TSK) fuzzy systems is presented. This characterization concerns the choice of the adequate conjunctive operator between input variables of discrete TSK fuzzy models, t-norm, and its impact on stability domain estimation. This new approach is based on stability conditions issued from vector norms corresponding to a vector-Lyapunov function. In particular, second order discrete TSK models are considered and this work concludes that Zadeh’s t-norm, logic product min, gives the largest estimation of stability domain.


Discrete nonlinear systems, discrete TSK fuzzy model, t-norm, stability domain, vector norm, arrow form matrix

Full Text:



Benrejeb M., Sakly A., Ben Othman K. and Borne P.: Choice of Conjunctive Operator of TSK Fuzzy Systems and Stability Domain Study. To appear in MATCOM (MAThematics and COMputers and simulation Journal).

Benrejeb M., Borne P. and Laurent F. : Sur une application de la représentation en flèche à l'analyse des processus. RAIRO Automatique, 16 (2). (1982) 133-146.

Borne P., Richard J. P. and Radhy N. E. : Stabilité, stabilisation, régulation : approche par les normes vectorielles, Systèmes non linéaires, tome 2 : stabilité-stabilisation. coordonné par Fossard A. J. et Normand-Cyrot D., Responsable du tome : Borne P., 45-90. Editions Masson, Paris (1993).

Butkiewicz B.S. : Control Error of Fuzzy System with Different Reasoning and Defuzzification Methods. 7th International Fuzzy Systems Association World Congress (IFSA) , III. Praga, Czech (1997).

Cao S. G., Rees N. W. and Feng G. : Quadratic stability analysis and design of continuous-time fuzzy control systems. Int. J. Syst. Sci., 27(2). (1996) 193-203.

Cardenas E., Castillo J.C., Cordon O., Herrera F. and Peregrin A. : Applicability of T-norms in Fuzzy Control. Busefal, 61. (1995) 28-37.

Gupta M.M. and Qi J. : Design of Fuzzy Logic Controllers Based on Generalized T-operators. Fuzzy Sets and Systems, 40. (1991) 473-489.

Palm R., Driankov D. and Hellendoorn H. : Model Based Fuzzy Control. Springer-Verlag, Berlin Heidelberg (1997).

Sakly A., Ben Othman K. and Benrejeb M. : Sur le Choix de l'Opérateur de Conjonction en Commande Floue Basé sur la Robustesse de Critères de Performances. 2ème Conférence Internationale JTEA, Tome 1, Sousse Nord (2002).

Sugeno M. : On stability of fuzzy systems expressed by fuzzy rules with singleton consequences. IEEE Transactions on Fuzzy Systems, 7(2). (1999) 201-223.

Tanaka K., Ikeda T. and Wang H.O. : Fuzzy Regulators and Fuzzy Observers : Relaxed Stability Conditions and LMI-based Designs. IEEE Transactions on Fuzzy Systems, 6(2). (1998) 1-16.

Tanaka K. and Sugeno M. : Stability analysis and design of fuzzy control systems. Fuzzy sets and systems, 45. (1992) 135-156.

Tanaka K. and Sano M. : A Robust Stabilization Problem of Fuzzy Control Systems and its Application to Backing up Control of a Truck-Trailer. IEEE Transactions on Fuzzy Systems, II. (1994) 119-134.

Yager R. R. and Filev D. P. : Essentials of Fuzzy Modeling and Control. John Wiley & Sons, Inc., USA (1994).


Copyright (c) 2017 Mohamed BENREJEB, Dhaou SOUDANI, Anis SAKLY, Pierre BORNE

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

CC-BY-NC  License for Website User

Articles published in IJCCC user license are protected by copyright.

Users can access, download, copy, translate the IJCCC articles for non-commercial purposes provided that users, but cannot redistribute, display or adapt:

  • Cite the article using an appropriate bibliographic citation: author(s), article title, journal, volume, issue, page numbers, year of publication, DOI, and the link to the definitive published version on IJCCC website;
  • Maintain the integrity of the IJCCC article;
  • Retain the copyright notices and links to these terms and conditions so it is clear to other users what can and what cannot be done with the  article;
  • Ensure that, for any content in the IJCCC article that is identified as belonging to a third party, any re-use complies with the copyright policies of that third party;
  • Any translations must prominently display the statement: "This is an unofficial translation of an article that appeared in IJCCC. Agora University  has not endorsed this translation."

This is a non commercial license where the use of published articles for commercial purposes is forbiden. 

Commercial purposes include: 

  • Copying or downloading IJCCC articles, or linking to such postings, for further redistribution, sale or licensing, for a fee;
  • Copying, downloading or posting by a site or service that incorporates advertising with such content;
  • The inclusion or incorporation of article content in other works or services (other than normal quotations with an appropriate citation) that is then available for sale or licensing, for a fee;
  • Use of IJCCC articles or article content (other than normal quotations with appropriate citation) by for-profit organizations for promotional purposes, whether for a fee or otherwise;
  • Use for the purposes of monetary reward by means of sale, resale, license, loan, transfer or other form of commercial exploitation;

    The licensor cannot revoke these freedoms as long as you follow the license terms.

[End of CC-BY-NC  License for Website User]

INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL (IJCCC), With Emphasis on the Integration of Three Technologies (C & C & C),  ISSN 1841-9836.

IJCCC was founded in 2006,  at Agora University, by  Ioan DZITAC (Editor-in-Chief),  Florin Gheorghe FILIP (Editor-in-Chief), and  Misu-Jan MANOLESCU (Managing Editor).

Ethics: This journal is a member of, and subscribes to the principles of, the Committee on Publication Ethics (COPE).

Ioan  DZITAC (Editor-in-Chief) at COPE European Seminar, Bruxelles, 2015:

IJCCC is covered/indexed/abstracted in Science Citation Index Expanded (since vol.1(S),  2006); JCR2018: IF=1.585..

IJCCC is indexed in Scopus from 2008 (CiteScore2018 = 1.56):

Nomination by Elsevier for Journal Excellence Award Romania 2015 (SNIP2014 = 1.029): Elsevier/ Scopus

IJCCC was nominated by Elsevier for Journal Excellence Award - "Scopus Awards Romania 2015" (SNIP2014 = 1.029).

IJCCC is in Top 3 of 157 Romanian journals indexed by Scopus (in all fields) and No.1 in Computer Science field by Elsevier/ Scopus.


 Impact Factor in JCR2018 (Clarivate Analytics/SCI Expanded/ISI Web of Science): IF=1.585 (Q3). Scopus: CiteScore2018=1.56 (Q2);

SCImago Journal & Country Rank

Editors-in-Chief: Ioan DZITAC & Florin Gheorghe FILIP.