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Journal Achievements of Modern Radioelectronics №10 for 2016 г.
Article in number:
Approaches to the analysis of stability of dynamic TS-systems on the basis of quadratic, piecewise quadratic and fuzzy Lyapunov functions
Keywords: dynamical TS-models stability stabilization Lyanunov functions
Authors:
V.I. Afanasyeva - Ph.D. (Phys.-Math.), Associate Professor, Russian Aviation Technology University named after K.E. Tsiolkovsky MATI, Moscow Aviation Institute (National Research University) E-mail: tualpin@list.ru О.V. Druzhinina - Dr.Sc. (Phys.-Math.), Professor, Chief Researcher, Federal Research Centre «Information and Control» of the Russian Academy of Sciences E-mail: ovdruzh@mail.ru S.N. Petrova - Ph.D. (Pedagogical), Associate Professor, Ural State Economical University, Technical University UMMC E-mail: axial_120@mail.ru
Abstract:
Approaches to the analysis of stability of Takagi-Sugeno systems (TS-systems), on the basis of quadratic, piecewise quadratic and fuzzy functions of Lyapunov are characterized. The review of results on stability of the models described by means of TS-systems is submitted. The perspectives of use of functions of Lyapunov for a research of qualitative behavior of the specified systems in problems of design and development of complex technical systems incloding electronic system are described.
Pages: 60-67
References

 

  1. Tanaka K., Sugeno V. Stability analysis and design of fuzzy control systems // Fuzzy Sets Syst. 1992. V. 45. № 2. R. 135-156.
  2. Tanaka K., Hori T., Wang H.O. A multiple Lyapunov function approach to stabilization of fuzzy control system // IEEE Trans. Fuzzy Syst. 2003. V. 11. № 4. R. 582-589.
  3. Vasilev S.N. K intellektnomu upravleniju // Nelinejjnaja teorija upravlenija i ee prilozhenija. M.: Fizmatlit. 2000. S. 57-126.
  4. Tanaka K., Wang H.O. Fuzzy Control Systems Design and Analisys. A Linear Matrix Inequalities Approach // New York: Wiley. 2001.
  5. Feng G. A survey on analysis and design of model-based fuzzy control systems // IEEE Trans. Fuzzy Syst. 2006. V. 14. № 5.P. 676-697.
  6. Pegat A. Nechetkoe modelirovanie i upravlenie. M.: BINOM. Laboratorijaznanijj. 2009.
  7. Han Z.X., Feng G., Walcott B.L., Ma J. Dynamic output feedback controller design for fuzzy systems // IEEE Trans. Syst., Man, Cybern. 2000. V. 30. № 1. P. 204-210.
  8. Kim E., Lee S. Output feedback tracking control of MIMO systems using a fuzzy disturbance observer and its application to the speed control of a PM synchronous motor // IEEE Trans. Fuzzy Syst. 2005. V. 13. № 6. P. 725-741.
  9. Abdelmalek I., Golea N., Hadjili M.L. A new fuzzy Lyapunov approach to non-quadratic stabilization of Takagi-Sugeno fuzzy models // Int. J. Appl. Math. Comput. Sci. 2007. V. 17. № 1. P. 39-51.
  10. Masina O.N., Druzhinina O.V., Afanaseva V.I. Analiz ustojjchivosti diskretnykh sistem upravlenija na osnove funkcijj Ljapunova i svojjstv linejjnykh matrichnykh neravenstv // Informacionno-izmeritelnye i upravljajushhie sistemy. 2011. T. 9. № 7. S. 49-58.
  11. Kang G., Lee W. Design of fuzzy state controllers and observers // Proc. Int. Joint Conf. 4th FUZZ-IEEE/2nd IFES. Yokohama. Japan. 1995. P. 1355-1360.
  12. Kim W.C., Ahn S.C., Kwon W.H. Stability analysis and stabilization of fuzzy state space models // Fuzzy Sets Syst. 1995. V. 71. № 1. P. 131-142.
  13. Akar M., Ozguner U. Decentralized techniques for the analysis and control of Takagi-Sugeno fuzzy systems // IEEE Trans. Fuzzy Syst. V. 8. № 6. P. 691-704.
  14. Fakhimi S., Fatehi A. Non-monotonic Lyapunov functions for stability analysis and stabilization of discrete time Takagi-Sugeno fuzzy systems // IJIC, Information and Control. 2014. V. 10. № 4. P. 1567-1586.
  15. Wang L., Liu X. New relaxed stabilization conditions for fuzzy control systems // International Journal of Innovative Computing, In formation and Control. 2009. V. 5. № 5. P. 1451-1460. "Uspekhisovremennojjradioehlektroniki", 2016 g., № 10 66
  16. Chen C.L., Feng G., Guan X.P. Delay-dependent stability analysis and controller synthesis for discrete time T-S fuzzy systems with time delays // IEEE Trans. Fuzzy Syst. 2005. V. 13. № 5. P. 630-643.
  17. Johansson M., Rantzer A., Arzen K.E. Piecewise quadratic stability of fuzzy systems // IEEE Trans. Fuzzy Syst. 1999. V. 7. № 6. P. 713-722.
  18. Kung C.C., Chen T.H., Chen C.H. H-infinity state feedback controller design for T-S fuzzy systems based on piecewise Lyapunov function // Proc. 14th IEEE Int. Conf. Fuzzy Systems, Reno. NV. May 2005. P. 708-713.
  19. Zamani I., Zarif M.H. An approach for stability analysis of T-S fuzzy systems via piecewise quadratic stability // International Journal of Innovative Computing, Information and Control. 2010. V. 6. № 9. P. 4041-4054.
  20. Wang Y., Sun Z.Q., Sun F.C. Stability analysis and control of discrete-time fuzzy systems: A fuzzy Lyapunov function approach // Proc. 5th Asian Control Conf., Melbourne. Australia. 2004. P.1855-1860.
  21. Johansen T.A. Fuzzy model based control: Stability robustness and performance issues // IEEE Trans. Fuzzy Syst. 1994. V. 2. № 1. P. 221-233.
  22. Park C.W., Cho Y.W. T-S model based indirect adaptive fuzzy control using online parameter estimation // IEEE Trans. Syst., Man, Cybern., B, Cybern. 2004. V. 34. № 6. P. 2293-2302.