Delay-dependent stability analysis and control synthesis of fuzzy dynamic systems with time delay. (English) Zbl 1106.93046

Summary: This paper focuses on the delay-dependent stability analysis and stabilization for fuzzy control systems with time delay. Based on linear matrix inequality (LMI) approach, a delay-dependent stability criteria has been developed. The design schemes of stabilization via state feedback is developed, and then the result is extended to the case of observer-based output feedback. All the researching results are presented by means of LMIs. Two illustrative examples are given to illustrate the validity of the proposed design procedures.


93D15 Stabilization of systems by feedback
93C42 Fuzzy control/observation systems
93B52 Feedback control
Full Text: DOI


[1] Cao, Y. Y.; Frank, P. M., Analysis and synthesis of nonlinear time-delay system via fuzzy control approach, IEEE Trans. Fuzzy Systems, 8, 2, 200-211 (2000)
[2] Cao, Y. Y.; Frank, P. M., Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy models, Fuzzy Sets and Systems, 124, 2, 213-229 (2001) · Zbl 1002.93051
[3] Chen, B.; Liu, X. P., Reliable control design of fuzzy dynamic systems with time-varying, Fuzzy Sets and Systems, 146, 3, 349-374 (2004) · Zbl 1055.93050
[4] Chen, B. S.; Tseng, C. S.; Uang, H. J., Mixed \(H_2 / H_\infty\) fuzzy output feedback control design for nonlinear dynamic systems: a LMI approach, IEEE Trans. Fuzzy Systems, 8, 3, 249-265 (2000)
[5] Esfahani, S. H.; Petersen, I. R., An LMI approach to output-feedback guaranteed cost control for uncertain time-delay systems, Internat. J. Robust Nonlinear Control, 10, 157-174 (2000) · Zbl 0951.93032
[6] Guan, X. P.; Chen, C. L., Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays, IEEE Trans. Fuzzy Systems, 12, 236-249 (2004) · Zbl 1142.93363
[7] Han, Q. L., Robust stability of uncertain delay-differential systems of neutral type, Automatica, 38, 719-723 (2002) · Zbl 1020.93016
[8] Jeung, E. T.; Oh, D. C.; Kim, J. H.; Park, H. B., Robust controller design for uncertain linear systems with time-varying delays: LMI approach, Automatica, 32, 8, 1229-1231 (1996) · Zbl 0854.93057
[9] Jun, Y.; Mashiro, N.; Hitoshi, K.; Akira, I., Output stabilization of Takagi-Sugeno fuzzy systems, Fuzzy Sets and Systems, 111, 253-266 (2000) · Zbl 0991.93069
[10] Lee, K. R.; Kim, J. H.; Jeung, E. T.; Park, H. B., Output feedback robust \(H_\infty\) control of uncertain fuzzy dynamic systems with time-varying delay, IEEE Trans. Fuzzy Systems, 8, 6, 657-664 (2000)
[11] Li, X.; De Souza, C. E., Criteria for robust stability and stabilization of uncertain linear systems with state delays, Automatica, 33, 9, 1657-1662 (1997) · Zbl 1422.93151
[12] Mahmoud, M. S., Robust \(H_\infty\) control of linear neutral systems, Automatica, 36, 757-764 (2000) · Zbl 0988.93024
[13] Shen, J. C., Designing stabilizing controller and observer for uncertain linear systems with time-delay, Automatica, 33, 4, 331-333 (1997) · Zbl 0885.93049
[14] Su, J. H., Further result on the robust stability of linear systems with a single time delay, Systems Control Lett., 23, 375-379 (1994) · Zbl 0805.93045
[15] Takagi, T., Stability and stabilizability of fuzzy-neural linear control systems, IEEE Trans. Fuzzy Systems, 3, 4, 438-447 (1995)
[16] 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
[17] Takagi, T.; Sugeno, M., Stability analysis and design of fuzzy control systems, Fuzzy Sets and Systems, 45, 2, 135-156 (1992) · Zbl 0758.93042
[18] Tanaka, K.; Ikeda, T.; Wang, H. O., Fuzzy regulator and fuzzy observer: relaxed stability conditions and lmi-based designs, IEEE Trans. Fuzzy Systems, 6, 2, 250-265 (1998)
[19] Tanaka, K.; Sano, M., A 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] Teixeira, M. C.; Zak, S. H., Stabilizing controller design for uncertain nonlinear systems using fuzzy models, IEEE Trans. Fuzzy Systems, 7, 2, 133-144 (1999)
[21] Tuan, H. D.; Apkarian, P.; Narikiyo, T.; Yamamoto, Y., Parameterized linear matrix inequality techniques in fuzzy control system design, IEEE Trans. Fuzzy Systems, 9, 2, 324-332 (2001)
[22] Wang, H. O.; Tanaka, K.; Griffin, M. F., An approach to fuzzy control of nonlinear systems: stability and design issues, IEEE Trans. Fuzzy Systems, 4, 1, 14-23 (1996)
[23] Zhang, Y.; Pheng, A. H., Stability of fuzzy systems with bounded uncertain delays, IEEE Trans. Fuzzy Systems, 10, 1, 92-97 (2002) · Zbl 1142.93377
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.