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Stability analysis of recurrent type-2 TSK fuzzy systems with nonlinear consequent part

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Abstract

A necessary condition for stability of a class of recurrent type-2 TSK fuzzy systems is presented. In this system, the antecedent part is indeed represented by interval Gaussian type-2 fuzzy set, and the consequent part is an ordinary nonlinear function of the system’s inputs. In the proposed method, at first a type-2 fuzzy model is established, and then an LMI-based stability analysis of the model is fully discussed. Two first-order systems (one stable and one unstable) and two second-order systems (one stable and one unstable) are then considered as proper case studies. The simulation results easily approve the effectiveness of the proposed method.

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References

  1. Sanchez MA, Castillo O, Castro JR (2015) Information granule formation via the concept of uncertainty-based information with interval type-2 fuzzy sets representation and Takagi–Sugeno–Kang consequents optimized with Cuckoo search. Appl Soft Comput 27:602–609

    Article  Google Scholar 

  2. Gaxiola F, Melin P, Valdez F, Castillo O (2014) Interval type-2 fuzzy weight adjustment for back propagation neural networks with application in time series prediction. Inf Sci 260:1–14

    Article  MATH  Google Scholar 

  3. Castillo O, Castro JR, Melin P, Díaz AR (2014) Application of interval type-2 fuzzy neural networks in non-linear identification and time series prediction. Soft Comput 18(6):1213–1224

    Article  Google Scholar 

  4. Castillo O, Castro JR, Melin P, Díaz AR (2013) Universal approximation of a class of interval type-2 fuzzy neural networks in nonlinear identification. Adv Fuzzy Syst 2013:1–16. Art ID 136214

    Article  MathSciNet  MATH  Google Scholar 

  5. Castro JR, Castillo O, Melin P, Díaz AR (2009) A hybrid learning algorithm for a class of interval type-2 fuzzy neural networks. Inf Sci 179(13):2175–2193

    Article  MATH  Google Scholar 

  6. Hagras HA (2004) A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots. IEEE Trans Fuzzy Syst 12(4):524–539

    Article  Google Scholar 

  7. Ozen T, Garibaldi JM (2003) Investigating adaptation in type-2 fuzzy logic systems applied to umbilical acid-base assessment. In: European symposium on intelligent technologies, hybrid systems and their implementation on smart adaptive systems, Oulu

  8. Méndez GM, Hernandez MA (2009) Hybrid learning for interval type-2 fuzzy logic systems based on orthogonal least-squares and back-propagation methods. Inf Sci 179(13):2146–2157

    Article  Google Scholar 

  9. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning. Parts 1, 2, and 3. Inf Sci 8:199–249

    Article  MATH  Google Scholar 

  10. Lam HK, Lauber J (2012) Stability analysis of nonlinear-function fuzzy model-based control systems. J Franklin Inst 349(10):3102–3120

    Article  MathSciNet  MATH  Google Scholar 

  11. Zamani I, Sadati N, Zarif MH (2011) On the stability issues for fuzzy large-scale systems. Fuzzy Sets Syst 174:31–49

    Article  MathSciNet  MATH  Google Scholar 

  12. Li J, Hu M, Guo L, Yang Y, Jin Y (2015) Stability of uncertain impulsive stochastic fuzzy neural networks with two additive time delays in the leakage term. Neural Comput Appl 26(2):417–427

    Article  Google Scholar 

  13. Lee DH, Park JB, Joo YH (2011) Approaches to extended non-quadratic stability and stabilization conditions for discrete-time Takagi Sugeno fuzzy systems. Automatica 47(3):534–538

    Article  MathSciNet  MATH  Google Scholar 

  14. Li X, Rakkiyappan R (2013) Stability results for Takagi-Sugeno fuzzy uncertain BAM neural networks with time delays in the leakage term. Neural Comput Appl 22(1):203–219

    Google Scholar 

  15. Suratgar AA, Nikravesh SK (2005) Potential energy based stability analysis of fuzzy linguistic systems. Iran J Fuzzy Syst 2(1):65–74

    MathSciNet  MATH  Google Scholar 

  16. Suratgar AA, Nikravesh SK (2009) A new method for linguistic modeling with stability analysis and applications. Intell Autom Soft Comput 15(3):329–342

    Article  Google Scholar 

  17. Mohan BM, Sinha A (2008) Analytical structure and stability analysis of a fuzzy PID controller. Appl Soft Comput 8:749–758

    Article  Google Scholar 

  18. Yang G (2014) New results on the stability of fuzzy cellular neural networks with time-varying leakage delays. Neural Comput Appl 25(7–8):1709–1715

    Article  Google Scholar 

  19. Chen L, Wu R, Pan D (2011) Mean square exponential stability of impulsive stochastic fuzzy cellular neural networks with distributed delays. Expert Syst Appl 38:6294–6299

    Article  Google Scholar 

  20. Long S, Xu D (2011) Stability analysis of stochastic fuzzy cellular neural networks with time varying delays. Neurocomputing 74:2385–2391

    Article  Google Scholar 

  21. Idrissi S, Tissir EH, Boumhidi I, Chaibi N (2013) New delay dependent robust stability criteria for T–S fuzzy systems with constant delay. Int J Control Autom Syst 11(5):885–892

    Article  Google Scholar 

  22. Ali MS (2014) Robust stability of stochastic fuzzy impulsive recurrent neural networks with time-varying delays. Iran J Fuzzy Syst 11(4):1–13

    MathSciNet  MATH  Google Scholar 

  23. Muralisankar S, Gopalakrishnan N (2014) Robust stability criteria for Takagi–Sugeno fuzzy Cohen–Grossberg neural networks of neutral type. Neurocomputing 144:516–525

    Article  MATH  Google Scholar 

  24. Lam HK, Seneviratne LD (2008) Stability analysis of interval type-2 fuzzy-model-based control systems. IEEE Trans Syst Man Cybern B Cybernet 38(3):617–628

    Article  Google Scholar 

  25. Biglarbegian M, Melek WW, Mendel JM (2009) On the stability of interval type-2 TSK fuzzy logic control systems. IEEE Trans Syst Man Cybern B Cybernet 40(3):798–818

    Article  Google Scholar 

  26. Jafarzadeh S, Sami Fadali M, Sonbol AH (2011) Stability analysis and control of discrete type-1 and type-2 TSK fuzzy systems: Part I. Stability analysis. IEEE Trans Fuzzy Syst 19(6):1001–1013

    Article  Google Scholar 

  27. Kumbasar T (2014) Robust stability analysis of PD type single input interval type-2 fuzzy control systems. In: IEEE International Conference on Fuzzy Systems, Beijing, China

  28. Yu WS, Chen HS (2014) Interval type-2 fuzzy adaptive tracking control design for PMDC motor with the sector dead-zones. Inf Sci 288:108–134

    Article  Google Scholar 

  29. El-Nagar AM, El-Bardini M (2014) Derivation and stability analysis of the analytical structures of the interval type-2 fuzzy PID controller. Appl Soft Comput 24:704–716

    Article  Google Scholar 

  30. Pan Y, Lib Y, Zhou Q (2014) Fault detection for interval type-2 fuzzy systems with sensor nonlinearities. Neurocomputing 145:488–494

    Article  Google Scholar 

  31. Ganjefar S, Solgi Y (2015) A Lyapunov stable type-2 fuzzy wavelet network controller design for a bilateral teleoperation system. Inf Sci 311:1–17

    Article  MathSciNet  Google Scholar 

  32. Cázarez N, Castillo O, Aguilar L, Cárdenas S (2007) From type-1 to type-2 fuzzy logic control: a stability and robustness study. Stud Fuzziness Soft Comput 208:135–149

    Article  MATH  Google Scholar 

  33. Castillo O, Aguilar L, Cázarez N, Melin P (2008) Systematic design of a stable type-2 fuzzy logic controller. Stud Fuzziness Soft Comput 218:319–331

    Article  Google Scholar 

  34. Morales J, Castillo O, Soria J (2008) Stability on type-1 and type-2 fuzzy logic systems. Stud Comput Intell 154:29–51

    Google Scholar 

  35. Nelles O (2001) Nonlinear system identification. Springer, Berlin Heidelberg

    Book  MATH  Google Scholar 

  36. Moodi H, Farrokhi M (2013) Robust observer design for Sugeno systems with incremental quadratic nonlinearity in the consequent. Int J Appl Math Comput Sci 23(4):711–723

    Article  MathSciNet  MATH  Google Scholar 

  37. Abiyev R, Mamedov F, Al-shanableh T (2007) Nonlinear neuro-fuzzy network for channel equalization. Anal Des Intell Syst Soft Comput Tech 41:327–336

    Article  Google Scholar 

  38. Tavoosi J, Badamchizadeh MA (2013) A class of type-2 fuzzy neural networks for nonlinear dynamical system identification. Neural Comput Appl 23(3):707–717

    Article  Google Scholar 

  39. Jahangiri F, Doustmohammadi A, Menhaj MB (2012) An adaptive wavelet differential neural networks based identifier and its stability analysis. Neurocomputing 77:12–19

    Article  Google Scholar 

  40. Dereli T, Baykasoglu A, Altun K, Durmusoglu A, Turksen IB (2011) Industrial applications of type-2 fuzzy sets and systems: a concise review. Comput Ind 62:125–137

    Article  Google Scholar 

  41. Mendel JM (2001) Uncertain rule-based fuzzy logic systems: introduction and new directions. Prentice-Hall, Englewood Cliffs, NJ

    MATH  Google Scholar 

  42. Castillo O, Melin P (2008) Type-2 fuzzy logic: theory and applications. Springer, Berlin Heidelberg

    MATH  Google Scholar 

  43. Karnik N, Mendel JM, Liang Q (1999) Type-2 fuzzy logic systems. IEEE Trans Fuzzy Syst 7(6):643–658

    Article  Google Scholar 

  44. Sontag ED (1997) Recurrent neural networks: Some systems-theoretic aspects. In: Karny M, Warwick K, Kurkova V (eds) Dealing with complexity: a neural network approach. Springer, London

    Google Scholar 

  45. Barabanov N, Prokhorov D (2002) Stability analysis of discrete time recurrent neural networks. IEEE Trans Neural Networks 13:292–303

    Article  Google Scholar 

  46. Chu Y, Glover K (1999) Bounds of the induced norm and model reduction errors for systems with repeated scalar nonlinearities. IEEE Trans Autom Control 44(2):471–483

    Article  MathSciNet  MATH  Google Scholar 

  47. Forssell U, Ljung L (2000) Identification of unstable systems using output error and Box–Jenkins model structures. IEEE Trans Autom Control 45(1):137–140

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Center of Excellence in Control and Robotics, Electrical Engineering Department, Amirkabir University of Technology, 424, Hafez Ave., Tehran, Iran

    Jafar Tavoosi, Amir Abolfazl Suratgar & Mohammad Bagher Menhaj

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  1. Jafar Tavoosi
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  2. Amir Abolfazl Suratgar
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  3. Mohammad Bagher Menhaj
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Correspondence to Amir Abolfazl Suratgar.

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Tavoosi, J., Suratgar, A.A. & Menhaj, M.B. Stability analysis of recurrent type-2 TSK fuzzy systems with nonlinear consequent part. Neural Comput & Applic 28, 47–56 (2017). https://doi.org/10.1007/s00521-015-2036-3

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  • DOI: https://doi.org/10.1007/s00521-015-2036-3

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