zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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:
93C42Fuzzy control systems
93D21Adaptive or robust stabilization
93C10Nonlinear control systems
93C73Perturbations in control systems
93B50Synthesis problems
93D09Robust stability of control systems
90C25Convex programming
Software:
LMI toolbox
WorldCat.org
Full Text: DOI
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. Proc. 3rd European congr. On intelligent techniques and soft computing, 565-569 (1995)
[3] Babuska, R.; Verbruggen, H. B.: A new identification method for linguistic fuzzy models. Proc. 4th IEEE conf. On fuzzy systems, 905-912 (1995)
[4] Barmish, B. R.: New tools for robustness of linear systems. (1994) · Zbl 1094.93517
[5] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in system and control theory. (1994) · 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. Proc. 4th IEEE internat. Conf. on fuzzy systems, 317-324 (1995)
[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)
[10] Kiriakidis, K.; Tzes, A.: Robust stability of linear systems against nonlinear time-varying perturbations. Preprints of the IFAC world congr., 263-268 (1996)
[11] Kuo, B. C.: Digital control systems. (1992)
[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. IFAC fuzzy information, 55-60 (1983)
[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. Proc. amer. Control conf., 2272-2280 (1995)
[22] Zhao, J.; Wertz, V.; Gorez, R.: Linear TS fuzzy model based robust stabilizing controller design. Proc. IEEE conf. On decision and control, 255-260 (1995)