zbMATH — the first resource for mathematics

Robust dynamic output feedback fuzzy Lyapunov stabilization of Takagi-Sugeno systems – a descriptor redundancy approach. (English) Zbl 1176.93045
Summary: This paper deals with Takagi-Sugeno (T-S) systems stabilization based on Dynamic Output Feedback Compensators (DOFC). In fact, only few results consider DOFC for T-S systems and most of them propose quadratic Lyapunov functions to provide stability conditions, which may lead to conservatism. In this work, to overcome this drawback and to enhance the closed-loop transient response, we provide for T-S uncertain closed-loop systems non-quadratic stability conditions. Based on a fuzzy Lyapunov candidate function and the descriptor redundancy property, these stability conditions are written in terms of Linear Matrix Inequalities (LMI). Afterward, the DOFC is designed with \(H_{\infty }\) criterion in order to minimize the influence of external disturbances. Finally, a few academic examples illustrate the efficiency of the proposed approaches.

93C42 Fuzzy control/observation systems
93D15 Stabilization of systems by feedback
93C15 Control/observation systems governed by ordinary differential equations
Full Text: DOI
[1] Apkarian, P.; Biannic, J.M.; Gahinet, P., Self-scheduled \(H_\infty\) control of a missile via linear matrix inequalities, J. guidance control dyn., 18, 3, 532-538, (1993)
[2] Assawinchaichote, W.; Nguang, S.K.; Shi, P., Output feedback control design for uncertain singularly perturbed systems: an LMI approach, Automatica, 40, 12, 2147-2152, (2004) · Zbl 1059.93504
[3] Ban, X.; Gao, X.Z.; Huang, X.; Vasilakos, A.V., Stability analysis of the simplest takagi – sugeno fuzzy control system using circle criterion, Inform. sci., 177, 20, 4387-4409, (2007) · Zbl 1120.93031
[4] Ban, X.; Gao, X.; Huang, X.; Yin, H., Stability analysis of the simplest takagi – sugeno fuzzy control system using Popov criterion, Internat. J. innovative comput. inform. control, 3, 5, 1087-1096, (2007) · Zbl 1126.93047
[5] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia, PA · Zbl 0816.93004
[6] Cao, S.G.; Rees, N.W.; Feng, G., \(H_\infty\) control of uncertain fuzzy continuous-time systems, Fuzzy sets and systems, 115, 2, 171-190, (2000) · Zbl 0960.93025
[7] Chen, B.S.; Tseng, C.S.; Uang, H.J., Mixed \(H_2 / H_\infty\) fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach, IEEE trans. fuzzy systems, 8, 3, 249-265, (2000)
[8] Feng, G., A survey on analysis and design of model-based fuzzy control systems, IEEE trans. fuzzy systems, 14, 5, 676-697, (2006)
[9] Fridman, E., New lyapunov – krasovskii functionals for stability of linear retarded and neutral type systems, Systems control lett., 43, 4, 309-319, (2001) · Zbl 0974.93028
[10] P. Gahinet, A. Nemirovski, A.J. Laub, M. Chilali, LMI control toolbox for use with MATLAB, The Mathworks Partner Series, 1995.
[11] K. Guelton, T. Bouarar, N. Manamanni, Fuzzy Lyapunov LMI based output feedback stabilization of Takagi-Sugeno systems using descriptor redundancy, in: Proc. FUZZ-IEEE 08, IEEE Internat. Conf. on Fuzzy Systems, Hong Kong, 2008. · Zbl 1176.93045
[12] 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, 12, 1414-1426, (2008)
[13] Guerra, T.M.; Vermeiren, L., LMI based relaxed nonquadratic stabilizations for non-linear systems in the takagi – sugeno’s form, Automatica, 40, 5, 823-829, (2004) · Zbl 1050.93048
[14] Guerra, T.M.; Kruszewski, A.; Vermeiren, L.; Tirmant, H., Conditions of output stabilization for nonlinear models in the takagi – sugeno’s form, Fuzzy sets and systems, 157, 9, 1248-1259, (2006) · Zbl 1090.93023
[15] T.M. Guerra, M. Bernal, A. Kruszewski, M. Afroun, A way to improve results for the stabilization of continuous-time fuzzy descriptor models, in: Proc. 46th IEEE Conf. on Decision and Control, New Orleans, USA, 2007.
[16] Huang, D.; Nguang, S.K., Robust \(H_\infty\) static output feedback control of fuzzy systems: an ILMI approach, IEEE trans. systems man cybernet. B, 36, 1, 216-222, (2006)
[17] Huang, D.; Nguang, S.K., Static output feedback controller design for fuzzy systems: an ILMI approach, Inform. sci., 177, 14, 3005-3015, (2007) · Zbl 1120.93334
[18] Johansson, M.; Rantzer, A.; Arzen, K.E., Piecewise quadratic stability of fuzzy systems, IEEE trans. fuzzy systems, 7, 6, 713-722, (1999)
[19] Kim, E.; Lee, H., New approaches to relaxed quadratic stability condition of fuzzy control systems, IEEE trans. fuzzy systems, 8, 5, 523-534, (2000)
[20] Li, J.; Wang, H.O.; Niemann, D.; Tanaka, K., Dynamic parallel distributed compensation for takagi – sugeno fuzzy systems: an LMI approach, Inform. sci., 123, 3-4, 201-221, (2000) · Zbl 0962.93060
[21] Liu, X.; Zhang, Q., New approaches to \(H_\infty\) controller design based on fuzzy observers for fuzzy T-S systems via LMI, Automatica, 39, 9, 1571-1582, (2003) · Zbl 1029.93042
[22] Manamanni, N.; Mansouri, B.; Hamzaoui, A.; Zaytoon, J., Relaxed conditions in tracking control design for T-S fuzzy model, J. intelligent fuzzy systems, 18, 2, 185-210, (2007) · Zbl 1134.93360
[23] B. Mansouri, A. Kruszewski, K. Guelton, N. Manamanni, Sub-optimal tracking control for uncertain T-S fuzzy models, in: Proc. AFNC 07, Third IFAC Workshop on Advanced Fuzzy and Neural Control, Valenciennes, France, 2007. · Zbl 1158.93024
[24] Mansouri, B.; Manamanni, N.; Guelton, K.; Kruszewski, A.; Guerra, T.M., Output feedback LMI tracking control conditions with \(H_\infty\) criterion for uncertain and disturbed T-S models, Inform. sci., 179, 4, 446-457, (2009) · Zbl 1158.93024
[25] Nguang, S.K.; Shi, P., Fuzzy \(H_\infty\) output feedback control of nonlinear systems under sampled measurements, Automatica, 39, 12, 2169-2174, (2003) · Zbl 1041.93033
[26] Nguang, S.K.; Shi, P., Robust output feedback control design for takagi – sugeno systems with Markovian jumps: a linear matrix inequality approach, J. dynamic systems measurement control, 128, 3, 617-625, (2006)
[27] Park, C.-W., LMI-based robust stability analysis for fuzzy feedback linearization regulators with its applications, Inform. sci., 152, 287-301, (2003) · Zbl 1035.93044
[28] Redheffer, R.M., On a certain linear fractional transformation, J. math. phys., 39, 269-286, (1960) · Zbl 0102.10402
[29] Rhee, B.J.; Won, S., A new Lyapunov function approach for a takagi – sugeno fuzzy control system design, Fuzzy sets and systems, 157, 9, 1211-1228, (2006) · Zbl 1090.93025
[30] Sala, A.; Guerra, T.M.; Babuska, R., Perspectives of fuzzy systems and control, Fuzzy sets and systems, 153, 3, 432-444, (2005), (Special Issue: 40th Anniversary of Fuzzy Sets) · Zbl 1082.93030
[31] Syrmos, V.L.; Abdallah, C.T.; Dorato, P.; Grigoriadis, K., Static output feedback—a survey, Automatica, 33, 2, 125-137, (1997) · Zbl 0872.93036
[32] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE trans. system man cybernet., 15, 1, 116-132, (1985) · Zbl 0576.93021
[33] Tanaka, K.; Sugeno, M., Stability analysis and design of fuzzy control systems, Fuzzy sets and systems, 45, 2, 135-156, (1992) · Zbl 0758.93042
[34] Tanaka, K.; Ikeda, T.; Wang, H.O., Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, \(H_\infty\) control theory, and linear matrix inequalities, IEEE trans. fuzzy systems, 4, 1, 1-13, (1996)
[35] Tanaka, K.; Ikeda, T.; Wang, H.O., Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs, IEEE trans. fuzzy systems, 6, 2, 1-16, (1998)
[36] Tanaka, K.; Wang, H.O., Fuzzy control systems design and analysis. A linear matrix inequality approach, (2001), Wiley New York
[37] Tanaka, K.; Hori, T.; Wang, H.O., A multiple Lyapunov function approach to stabilization of fuzzy control systems, IEEE trans. fuzzy systems, 11, 4, 582-589, (2003)
[38] Tanaka, K.; Ohtake, H.; Wang, H.O., A descriptor system approach to fuzzy control system design via fuzzy Lyapunov functions, IEEE trans. fuzzy systems, 15, 3, 333-341, (2007)
[39] Tong, S.; Li, Y., Direct adaptive fuzzy backstepping control for a class of nonlinear systems, Int. J. innovative comput. inform. control, 3, 4, 887-896, (2007)
[40] Tong, S.; Wang, W.; Qu, L., Decentralized robust control for uncertain T-S fuzzy large-scale systems with time-delay, Int. J. innovative comput. inform. control, 3, 3, 657-672, (2007)
[41] Tuan, H.D.; Apkarian, P.; Narikiyo, T.; Yamamoto, Y., Parametrized linear matrix inequality techniques in fuzzy control design, IEEE trans. fuzzy systems, 9, 324-332, (2001)
[42] Wang, H.O.; Tanaka, K.; Griffin, M.F., An approach to fuzzy control of nonlinear systems: stability and the design issues, IEEE trans. fuzzy systems, 4, 1, 14-23, (1996)
[43] Xu, S.; Lam, J., Robust \(H_\infty\) control for uncertain discrete-time-delay fuzzy systems via output feedback controllers, IEEE trans. fuzzy systems, 13, 1, 82-93, (2005)
[44] Yoneyama, J.; Nishikawa, M.; Katayama, H.; Ichikawa, A., Output stabilization of takagi – sugeno fuzzy systems, Fuzzy sets and systems, 111, 2, 253-266, (2000) · Zbl 0991.93069
[45] Yoneyama, J.; Nishikawa, M.; Katayama, H.; Ichikawa, A., Design of output feedback controllers for takagi – sugeno fuzzy systems, Fuzzy sets and systems, 121, 127-148, (2001) · Zbl 0991.93068
[46] Zerar, M.; Guelton, K.; Manamanni, N., Linear fractional transformation based H-infinity output stabilization for takagi – sugeno fuzzy models, Mediterranean J. measurement control, 4, 3, 111-121, (2008)
[47] Zhou, K.; Khargonekar, P.P., Robust stabilization of linear systems with norm-bounded time-varying uncertainty, Systems control lett., 10, 1, 17-20, (1988) · Zbl 0634.93066
[48] Zhou, K.; Doyle, J.; Glover, K., Robust and optimal control, (1996), Prentice-Hall New Jersey
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.