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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.

MSC:
93C42Fuzzy control systems
93D10Popov-type stability of feedback systems
93C80Frequency-response methods
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References:
[1] Byrnes, I.; Isidori, A.; Williems, J. C.: Passivity, feedback equivalence and the global stabilization of minimum phase nonlinear systems. IEEE tans. Automat. control 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) · 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) · 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) · 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)
[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 14, 345-349 (1984)
[16] Vidyasagar, M.: Nonlinear systems analysis. (1993) · 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