Abstract
This chapter is concerned with recent developments on observer design for non-linear systems via Takagi-Sugeno models, both in continuous- and discrete-time. As traditionally done, the direct Lyapunov method is employed to derive conditions in the form of linear matrix inequalities. Novelties include a better handling of measurable and unmeasurable premises, the inclusion of multiple delays in non-quadratic Lyapunov functions, and the use of matrix properties to add slack variables; feasibility of conditions is thus enhanced while improving the quality of solutions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bergsten, P., Palm, R., Driankov, D.: Fuzzy observers. In: 2001 The 10th IEEE International Conference on Fuzzy Systems, pp. 700–703 (2001)
Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear matrix inequalities in system and control theory. Soc. Ind. Math. (1994)
Chadli, M., Karimi, H.R.: Robust observer design for unknown inputs Takagi–Sugeno models. IEEE Trans. Fuzzy Syst. 21(1), 158–164 (2013)
Gahinet, P., Nemirovski, A., Laub, A.J., Chilali, M.: LMI Control Toolbox. The Math Works Inc., Massachusetts (1995)
Guelton, K., Delprat, S., Guerra, T.M.: An alternative to inverse dynamics joint torques estimation in human stance based on a Takagi-Sugeno unknown-inputs observer in the descriptor form. Control Eng. Practice 16, 1414–1426 (2008)
Guerra, T.M., Estrada-Menzo, V., Lendek, Z.: Observer design for Takagi-Sugeno descriptor models: an LMI approach. Automatica 52, 154–159 (2015)
Guerra, T.M., Vermeiren, L.: LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi–Sugeno’s form. Automatica 40(5), 823–829 (2004)
Guerra, T.M., Kerkeni, H., Lauber, J., Vermeiren, L.: An efficient Lyapunov function for discrete TS models: observer design. IEEE Trans. Fuzzy Syst. 20(1), 187–192 (2012)
Guerra, T.M., Kruszewski, A., Vermeiren, L., Tirmant, H.: Conditions of output stabilization for nonlinear models in the Takagi-Sugeno’s form. Fuzzy Sets Syst. 157(9), 1248–1259 (2006)
Guerra, T.M., Marquez, R., Kruszewski, A., Bernal, M.: H∞ LMI-based observer design for nonlinear systems via TS models with unmeasured premise variables. IEEE Trans. Fuzzy Syst. 26(3), 1498–1509 (2017)
Ichalal, D., Marx, B., Maquin, D., Ragot, J.: Observer design and fault tolerant control of Takagi-Sugeno nonlinear systems with unmeasurable premise variables. In: Fault Diagnosis in Robotic and Industrial Systems, pp. 1–21 (2012)
Ichalal, D., Marx, B., Maquin, D., Ragot, J.: On observer design for nonlinear Takagi-Sugeno systems with unmeasurable premise variable. In: International Symposium on Advanced Control of Industrial Processes, pp. 353–358. IEEE (2011)
Ichalal, D., Marx, B., Ragot, J., Maquin, D.: Conception d’observateurs pour un modèle de Takagi-Sugeno à variables de décision non mesurables. In: 8ème Conférence Internationale Sciences et Techniques de l’Automatique (2007)
Kruszewski, A., Wang, R., Guerra, T.M.: Nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time TS fuzzy models: a new approach. IEEE Trans. Autom. Control 53(2), 606–611 (2008)
Lam, H.K., Keung, A.: Stability Analysis of Fuzzy-Model-Based Control Systems, vol. 264, 226 pp. Springer-Verlag, Berlin, Heidelberg (2010)
Lendek, Z., Guerra, T.M., Babuska, R., De Schutter, B.: Stability Analysis and Nonlinear Observer Design Using Takagi-Sugeno Fuzzy Models, vol. 262, 196 pp. Springer, Berlin, Heidelberg (2010)
Lendek, Z., Lauber, J., Guerra, T.-M., Babuska, R., De Schutter, B.: Adaptive observers for TS fuzzy systems with unknown polynomial inputs. Fuzzy Sets Syst. 161, 2043–2065 (2010)
Márquez, R., Guerra, T.M., Bernal, M., Kruszewski, A.: Asymptotically necessary and sufficient conditions for Takagi-Sugeno models using generalized non-quadratic parameter-dependent controller design. Fuzzy Sets Syst. 306, 48–62 (2017)
Peaucelle, D., Arzelier, D., Bachelier, O., Bernussou, J.: A new robust D-stability condition for real convex polytopic uncertainty. Syst. Control Lett. 40, 21–30 (2000)
Sala, A., Ariño, C.: Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: applications of Polya’s theorem. Fuzzy Sets Syst. 158(24), 2671–2686 (2007)
Sturm, J.F.: Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optim. Methods Softw. 11(1–4), 625–653 (1999)
Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. 1, 116–132 (1985)
Tanaka, K., Wang, H.O.: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. Wiley (2001)
Taniguchi, T., Tanaka, K., Ohtake, H., Wang, H.O.: Model construction, rule reduction, and robust compensation for generalized form of Takagi-Sugeno fuzzy systems. IEEE Trans. Fuzzy Syst. 9(4), 525–538 (2001)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Guerra, TM., Bernal, M.A. (2021). Control: Advances on Fuzzy Model-Based Observers. In: Lesot, MJ., Marsala, C. (eds) Fuzzy Approaches for Soft Computing and Approximate Reasoning: Theories and Applications. Studies in Fuzziness and Soft Computing, vol 394. Springer, Cham. https://doi.org/10.1007/978-3-030-54341-9_16
Download citation
DOI: https://doi.org/10.1007/978-3-030-54341-9_16
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-54340-2
Online ISBN: 978-3-030-54341-9
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)