Passivity approach to fuzzy control systems. (English) Zbl 0919.93047

Many fuzzy controllers can be viewed as nonlinear controllers characterized by a bounded continuous input-output mapping with some symmetry properties. The paper shows that passivity theory forms a fruitful framework for the stability analysis of such fuzzy controllers. For linear time-invariant continuous-time controlled systems, the passivity approach leads to frequency response conditions similar to previous results in the literature. However, more general signals can be considered here, and the stability conditions can be strengthened to include robustness with respect to uncertainties in the controlled system.
Reviewer: J.Virtanen (Vaasa)


93C42 Fuzzy control/observation systems
93D10 Popov-type stability of feedback systems
93C80 Frequency-response methods in control theory
Full Text: DOI


[1] Byrnes, I.; Isidori, A.; Williems, J.C., Passivity, feedback equivalence and the global stabilization of minimum phase nonlinear systems, IEEE tans. automat. control, AC 36, 1228-1240, (1991) · Zbl 0758.93007
[2] Calcev, G., (1993). Stability analysis of a fuzzy control system: a frequency approach. In Proc. CSCS1: 9th Int. Conf. on Control Systems and Computer Science, Bucharest, Romania, pp. 252-257.
[3] Commuri, S.; Lewis, F.L., Cmac neural networks for control of nonlinear dynamical systemsstructure, stability and passivity, Automatica, 33, 635-641, (1997) · Zbl 0883.93045
[4] De Neyer, M.; Gorez, R., Comments on practical design of nonlinear fuzzy controllers with stability analysis for regulating processes with unknown mathematical models, Automatica, 32, 1613-1614, (1996) · Zbl 0875.93240
[5] Desoer, C.A.; Vidyasagar, M., Feedback systemsinput-output properties, (1975), Academic Press New York · Zbl 0327.93009
[6] Hill, D.J.; Moylan, P.J., Stability results for nonlinear feedback systems, Automatica, 13, 377-382, (1977) · Zbl 0356.93025
[7] Hill, D. J., (1992). Dissipative nonlinear systems: basic properties and stability analysis. In Proc. 31th IEEE CDC, pp.3259-3264.
[8] Lefschetz, S., Stability of nonlinear control systems, (1965), Academic Press New York · Zbl 0136.08801
[9] Lim, J.T., Absolute stability of class of nonlinear plants with fuzzy logic controllers, Electron. lett, 28, 1968-1970, (1992)
[10] Lewis, F.L.; Liu, K., Towards a paradigm for fuzzy logic control, Automatica, 32, 167-181, (1996) · Zbl 0845.93048
[11] Melin, C., (1995). Stability analysis of fuzzy control systems: some frequency criteria. In Proc. ECC’95: 3rd European Control Conf., Roma, Italy, pp.815—819.
[12] Narendra, K.S.; Taylor, J.H., Frequency domain criteria for absolute stability, (1973), Academic Press New York · Zbl 0266.93037
[13] Opitz, H. P., (1993). Fuzzy-control and stability criteria. In Proc. EUFIT ’93, Aachen, Germany, pp.130—135.
[14] Popov, V.M., Hiperstabilitatea sistemelor automate, (1966), Edit. Academiei Bucharest, Romania
[15] Ray, K.; Majumder, D.D., Application of circle criteria for stability analysis of linear SISO and MIMO systems associated with fuzzy logic controller, IEEE trans. system man cybernet, SMC 14, 345-349, (1984)
[16] Vidyasagar, M., Nonlinear systems analysis, (1993), Prentice-Hall Englewood Cliffs, NJ · Zbl 0900.93132
[17] Ying, H., Practical design of nonlinear fuzzy controllers with stability analysis for regulating processes with unknown mathematical models, Automatica, 30, 1185-1195, (1994) · Zbl 0800.93711
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.