## Quadratic stability analysis of the Takagi-Sugeno fuzzy model.(English)Zbl 0929.93024

Summary: The nonlinear dynamic Takagi-Sugeno fuzzy model with offset terms is analyzed as a perturbed linear system. A sufficient criterion for the robust stability of this nominal system against nonlinear perturbations guarantees quadratic stability of the fuzzy model. The criterion accepts a convex programming formulation of reduced computational cost compared to the common Lyapunov matrix approach. Parametric robust control techniques suggest synthesis tools for stabilization of the fuzzy system. Application examples on fuzzy models of nonlinear plants advocate the efficiency of the method. The examples demonstrate reduced conservatism compared to norm-based criteria.

### MSC:

 93C42 Fuzzy control/observation systems 93D21 Adaptive or robust stabilization 93C10 Nonlinear systems in control theory 93C73 Perturbations in control/observation systems 93B50 Synthesis problems 93D09 Robust stability 90C25 Convex programming

LMI toolbox
Full Text:

### References:

 [1] Ackermann, J., Parameter space design of robust control systems, IEEE trans. automat. control, 25, 1058-1072, (1980) · Zbl 0483.93041 [2] Babuska, R.; Kaymak, U., Application of compatible cluster merging to fuzzy modeling of multivariable systems, (), 565-569 [3] Babuska, R.; Verbruggen, H.B., A new identification method for linguistic fuzzy models, (), 905-912 [4] Barmish, B.R., New tools for robustness of linear systems, (1994), MacMillan New York · Zbl 1094.93517 [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] Gao, S.G.; Rees, N.W., Identification of dynamic fuzzy models, Fuzzy sets and systems, 74, 307-320, (1995) · Zbl 0852.93049 [7] Cao, S.G.; Rees, N.W., Analysis and design of fuzzy control systems, (), 317-324 [8] Cao, S.G.; Rees, N.W.; Feng, G., Analysis and design of fuzzy control systems using dynamic fuzzy global models, Fuzzy sets and systems, 75, 47-62, (1995) · Zbl 0852.93050 [9] Gahinet, P.; Nemirovski, A.; Laub, A.; Chilali, M., LMI control toolbox, (1995), The MathWorks Inc Natick, MA [10] Kiriakidis, K.; Tzes, A., Robust stability of linear systems against nonlinear time-varying perturbations, (), 263-268 [11] Kuo, B.C., Digital control systems, (1992), Saunders College Publishing Orlando, FL [12] Mori, T.; Kokame, H., Convergence property of interval matrices and interval polynomials, Internat. J. control, 45, 481-484, (1987) · Zbl 0617.65041 [13] Sugeno, M.; Kang, G.T., Fuzzy modeling and control of multilayer incinerator, Fuzzy sets and systems, 18, 329-346, (1986) · Zbl 0612.93022 [14] Sugeno, M.; Kang, G.T., Structure identification of fuzzy model, Fuzzy sets and systems, 28, 15-33, (1988) · Zbl 0652.93010 [15] Sugeno, M.; Tanaka, K., Successive identification of a fuzzy model and its application to prediction of a complex system, Fuzzy sets and systems, 42, 315-334, (1991) · Zbl 0741.93052 [16] Sugeno, M.; Yasukawa, T., A fuzzy-logic-based approach to qualitative modeling, IEEE trans. fuzzy systems, 1, 7-31, (1993) [17] Takagi, T.; Sugeno, M., Derivation of fuzzy control rules from human Operator’s control action, (), 55-60 [18] Takagi, T.; Sugeno, M., Fuzzy identification of systems and its applications to modeling and control, IEEE trans. systems man cybernet., 15, 116-132, (1985) · Zbl 0576.93021 [19] Tanaka, K.; Sano, M., Robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer, IEEE trans. fuzzy systems, 2, 119-134, (1994) [20] Tanaka, K.; Sugeno, M., Stability analysis and design of fuzzy control systems, Fuzzy sets and systems, 45, 135-156, (1992) · Zbl 0758.93042 [21] Wang, H.O.; Tanaka, K.; Griffin, M., Parallel distributed compensation of nonlinear systems by Takagi-sugeno fuzzy model, (), 2272-2280 [22] Zhao, J.; Wertz, V.; Gorez, R., Linear TS fuzzy model based robust stabilizing controller design, (), 255-260
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.