Previous |  Up |  Next


fuzzy models; nonquadratic stabilization; nonlinear control; Lyapunov function; linear matrix inequality (LMI)
This paper presents a relaxed scheme for controller synthesis of continuous- time systems in the Takagi-Sugeno form, based on non-quadratic Lyapunov functions and a non-PDC control law. The relaxations here provided allow state and input dependence of the membership functions’ derivatives, as well as independence on initial conditions when input constraints are needed. Moreover, the controller synthesis is attainable via linear matrix inequalities, which are efficiently solved by commercially available software.
[1] Apkarian X., Gahinet X.: A convex characterization of gain scheduling Hinf controllers. IEEE Trans. Control Systems 40 (1995), 853–864 MR 1328081
[2] Begovich O., Sanchez E. N., Maldonado M.: Takagi–Sugeno fuzzy scheme for real trajectory tracking of an underactuated robot. IEEE Trans. Control Systems Techn. 10 (2002), 14–20 DOI 10.1109/87.974334
[3] Bernal M., Hušek P.: Piecewise quadratic stability of affine Takagi–Sugeno fuzzy control systems. In: Proc. Advanced Fuzzy-Neural Control Conference, Oulu 2004, pp.157–162
[4] Bernal M., Hušek P.: Controller synthesis with input and output constraints for fuzzy systems. In: 16th IFAC World Congress DVD-edition, Prague 2005
[5] Bernal M.: Non-quadratic discrete fuzzy controller design performing decay rate. In: FUZZ–IEEE Internat. Conference, Reno 2005, CD edition
[6] Bernal M., Hušek, P., Kučera V.: Non-quadratic design for continuous-time systems in the Takagi–Sugeno form. Submitted to Automatica
[7] Feng G.: Controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions. IEEE Trans. Fuzzy Systems 11 (2003), 605–612 DOI 10.1109/TFUZZ.2003.817837
[8] Feng G.: Stability analysis of discrete time fuzzy dynamic systems based on piecewise Lyapunov functions. IEEE Trans. Fuzzy Systems 12 (2004), 22–28 DOI 10.1109/TFUZZ.2003.819833
[9] Guerra T. M., Vermeiren L.: LMI-based relaxed non-quadratic stabilization conditions for nonlinear systems in Takagi–Sugeno’s form. Automatica 40 (2004), 823–829 DOI 10.1016/j.automatica.2003.12.014 | MR 2152188
[10] Johansson M., Rantzer, A., Arzen K.: Piecewise quadratic stability of fuzzy systems. IEEE Trans. Fuzzy Systems 7 (1999), 713–722 DOI 10.1109/91.811241
[11] Rantzer A., Johansson M.: Piecewise linear quadratic optimal control. IEEE Trans. Automat. Control 45 (2000), 629–637 DOI 10.1109/9.847100 | MR 1764832 | Zbl 0969.49016
[12] Takagi T., Sugeno M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Systems, Man and Cybernet. 15 (1985), 116–132 DOI 10.1109/TSMC.1985.6313399 | Zbl 0576.93021
[13] Tanaka K., Sugeno M.: Stability analysis of fuzzy systems using Lyapunov’s direct method. In: Proc. NAFIPS’90, pp. 133–136
[14] Tanaka K., Ikeda, T., Wang H. O.: Fuzzy regulators and fuzzy observers: Relaxed stability conditions and lmi-based designs. IEEE Trans. Fuzzy Systems 6 (1998), 250–264 DOI 10.1109/91.669023
[15] Tanaka K., Hori, T., Wang H. O.: A multiple function approach to stabilization of fuzzy control systems. IEEE Trans. Fuzzy Systems 11 (2003), 582–589 DOI 10.1109/TFUZZ.2003.814861
[16] H. O. Wang , Tanaka, K., Griffin M.: An approach to fuzzy control of nonlinear systems: Stability and design issues. IEEE Trans. Fuzzy Systems 4 (1996), 14–23 DOI 10.1109/91.481841
Partner of
EuDML logo