Approaches to the analysis of stability of dynamic TS-systems on the basis of quadratic, piecewise quadratic and fuzzy Lyapunov functions

V.I. Afanasyeva; О.V. Druzhinina; S.N. Petrova

Approaches to the analysis of stability of dynamic TS-systems on the basis of quadratic, piecewise quadratic and fuzzy Lyapunov functions

V.I. Afanasyeva¹, О.V. Druzhinina², S.N. Petrova³

research article Pages: 60-67

¹ Ph.D. (Phys.-Math.), Associate Professor, Russian Aviation Technology University named after K.E. Tsiolkovsky MATI, Moscow Aviation Institute (National Research University)
² Dr.Sc. (Phys.-Math.), Professor, Chief Researcher, Federal Research Centre «Information and Control» of the Russian Academy of Sciences
³ Ph.D. (Pedagogical), Associate Professor, Ural State Economical University, Technical University UMMC

Keywords: dynamical TS-models stability stabilization Lyanunov functions

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.

How to cite

Афанасьева В.И., Дружинина О.В., Петрова С.Н. Подходы к анализу устойчивости динамических ТС-систем на основе квадратичных, кусочно-квадратичных и нечетких функций Ляпунова // Успехи современной радиоэлектроники. 2016. № 10. С. 60–67.

References

Tanaka K., Sugeno V. Stability analysis and design of fuzzy control systems // Fuzzy Sets Syst. 1992. V. 45. № 2. R. 135-156.
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.
Vasilev S.N. K intellektnomu upravleniju // Nelinejjnaja teorija upravlenija i ee prilozhenija. M.: Fizmatlit. 2000. S. 57-126.
Tanaka K., Wang H.O. Fuzzy Control Systems Design and Analisys. A Linear Matrix Inequalities Approach // New York: Wiley. 2001.
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.
Pegat A. Nechetkoe modelirovanie i upravlenie. M.: BINOM. Laboratorijaznanijj. 2009.
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
Johansson M., Rantzer A., Arzen K.E. Piecewise quadratic stability of fuzzy systems // IEEE Trans. Fuzzy Syst. 1999. V. 7. № 6. P. 713-722.
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.
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.
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.
Johansen T.A. Fuzzy model based control: Stability robustness and performance issues // IEEE Trans. Fuzzy Syst. 1994. V. 2. № 1. P. 221-233.
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.

[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.

Abstract

How to cite

Related articles