Application of inverse system for linearization and decoupling. (English) Zbl 0634.93039

Summary: We show that for a special class of nonlinear systems the linearization and/or decoupling of nonlinear dynamics by immersion under feedback is in fact an application of the right inverse system.


93C10 Nonlinear systems in control theory
93B15 Realizations from input-output data
93C15 Control/observation systems governed by ordinary differential equations
93B27 Geometric methods
Full Text: DOI


[1] Claude, D.; Fliess, M.; Isidori, A., Immersion, directe et par bouclage, d’un système nonlineaire dans un lineaire, CR. acad. sci. Paris ser. I, 296, 237-240, (1983) · Zbl 0529.93030
[2] Isidori, A.; Ruberti, A., On the synthesis of linear input-output responses for nonlinear systems, Systems control lett., 4, 17-22, (1984) · Zbl 0551.93032
[3] Isidori, A., The matching of a prescribed linear input-output behavior in a nonlinear system, IEEE trans. automat. control, 30, 258-265, (1985) · Zbl 0564.93032
[4] Claude, D., Decoupling of nonlinear systems, Systems control lett., 1, 242-248, (1982) · Zbl 0473.93043
[5] Isidori, A.; Krener, A.J.; Gori-Giorgi, C.; Monaco, S., Nonlinear decoupling via feedback: a differential geometric approach, IEEE trans. automat. control, 26, 331-345, (1981) · Zbl 0481.93037
[6] Fliess, M., Finite-dimensional observation-spaces for non-linear systems, (), 73-77
[7] Fliess, M.; Kupka, I., A finiteness criterion for nonlinear input-output differential systems, SIAMJ. control optim., 21, 721-728, (1983) · Zbl 0529.93031
[8] Hirschorn, R.M., Output tracking in multivariable nonlinear systems, IEEE trans. automat. control, 26, 593-595, (1981) · Zbl 0477.93010
[9] Silverman, L.M., Inversion of multivariable linear systems, IEEE trans. automat. control, 14, 270-276, (1969)
[10] Hirschorn, R.M., Invertibility of multivariable nonlinear control systems, IEEE trans. automat. control, 24, 855-866, (1979) · Zbl 0427.93020
[11] Graybill, F.A., Introduction to matrices with applications in statistics, (1969), Wadsworth Belmont, CA · Zbl 0188.51601
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.