350 rub
Journal Information-measuring and Control Systems №6 for 2012 г.
Article in number:
Method of Lyapunov Functions for Nonquadratic Stabilization of Controlled Systems
Keywords: Takagi-Sugeno systems stability conditions linear matrix inequalities Lyapunov's function stabilization
Authors:
O.V. Druzhininа, S.N. Petrova
Abstract:
On the basis of the scheme of in parallel distributed compensation for stabilization of TakagiSugeno system the method of obtaining of conditions of nonquadratic stability is offered. Nonquadratic Lyapunov's function is presented in the form of a set of several Lyapunov functions. The offered stability conditions are less restrictive in comparison with known and also allow to stabilize the fuzzy systems which are not supposing the quadratic stabilization. The new stability conditions of TS-model based on using of several Lyapunov functions are obtained. It is shown that sufficient stability conditions of system can be formulated in terms of an admissibility of a set of linear matrix inequalities. The given method allows to use the structural information in base of the rules reducing restrictiveness of analysis and to increase the efficiency of calculations.
Pages: 42-49
References
  1. Tanaka K., Sugeno V. Stability analysis and design of fuzzy control sysnems// Fuzzy Sets Syst. 1992. V. 45. № 2. Р. 135-156.
  2. Tanaka K., Hori T., Wang H.O. A fuzzy Lyapunov approach to fuzzy control system design // Proc. American Conf., Arlington VA, Washington CD. 2001. Р. 4790 - 4795.
  3. Tanaka K., Hori T., Wang H.O. New parallet distributed compensation using time derivative membership functions: A fuzzy Lyapunov approach // Proc. 40th IEEE Conf. Decision and Control, Oregano, FL. 2001. Р. 3942 - 3947.
  4. 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. Р. 582 - 589.
  5. Васильев С.Н. К интеллектному управлению // Нелинейная теория управления и ее приложения. М.: Физматлит. 2000. С. 57-126.
  6. Tanaka K., Wang H.O. Fuzzy Control Systems Design and Analisys. A Linear Matrix Inequalities Approach // New York:
    Wiley. 2001.
  7. Wong L.K. Leung F.H.F., Tam P.K.S. Lyapunov-function-based design of fuzzy logic controllers and its application on combining controllers // IEEE Trans. Industr. Electron. 1998. V. 45. № 3. Р. 502 - 509.
  8. Tanaka K., Hori T., Wang H.O. A dual design problem via multiple Lyapunov function // Proc. 10th IEEE Int. Conf. FuzzySystem, Melbourne, Australia. 2001.
  9. Пегат А.Нечеткое моделирование и управление. М.: БИНОМ. Лаборатория знаний. 2009.
  10. Гостев В.И. Нечеткие регуляторы в системах автоматического управления. Киев: Радiоматор. 2008.
  11. Wang H.O., Tanaka K., Griffin M. Parallel distributed compensation of nonlinear systems by Takagi and Sugeno's  fuzzy  model // Proc. 4th IEEE Int. Conf. Fuzzy Systems. Yokohama, Japan. 1995. Р. 531-538.
  12. Korba P., Babuska R., Verbruggen H.B., Frank P.M. Fuzzy gain scheduling: controller and observer design based on Lyapunov method and convex optimization // IEEE Trans. Fuzzy Syst. 2003. V. 11. № 3. Р. 285-298.
  13. Bernal M.,  Husek P. Non-quadratic performance design for Takagi - Sugeno fuzzy system // Int. J. Appl. Math. Comput. Sci. 2005.  V. 15. № 3. Р. 383 - 391.
  14. Петрова С.Н. Об использовании параметризованных линейных матричных неравенств для синтеза и стабилизации нечетких систем управления // Труды Междунар. конф. «Управление в технических системах». СПб.: ГНЦРФЦНИИ «Электроприбор». 2010. С. 127-128.
  15. Chadli M., Maquin D., Ragot J. Relaxed stability conditions for Takagi-Sugeno fuzzy systems // Proc. IEEE Int. Conf. Systems,  Man and Cybernetics, SMC, Nashville, TN. 2000. Р. 3514 - 3519.
  16. Chadli M., Maquin D., Ragot J. On the stability analisis of multiplr model systems // Proc. European Control Conferense,  ECCC, Porto, Portugal. 2001. Р. 1894-1899.
  17. Chadli M., Maquin D., Ragot J. Stability analysis and design for continuos-time Takagi-Sugeno control systems // Int. J. Fuzzy Syst. 2005. V. 7. № 3.  Р. 101-109.