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Local observability of nonlinear systems. (English) Zbl 0877.93010
Summary: A necessary and sufficient condition for local observability of analytic systems is presented. For smooth systems this condition is only sufficient, but it is still weaker than the Hermann-Krener rank condition. It is expressed with the language of ideals of germs of analytic or smooth functions and real radicals of such ideals. The condition may be practically checked in many cases.

MSC:
93B07Observability
93B29Differential-geometric methods in systems theory (MSC2000)
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References:
[1] Bochnak, J.; Coste, M.; Roy, M-F.: Géométrie algébrique réelle. (1987)
[2] P. Crouch, Lecture Notes on Geometric Nonlinear Systems Theory, Control Theory Centre Report No. 99, Warwick University.
[3] Forsman, K.: Some generic results on algebraic observability and connections with realization theory. Proc. 2nd European control conf., 1185-1190 (1993)
[4] Gunning, R. C.; Rossi, H.: Analytic functions of several complex variables. (1965) · Zbl 0141.08601
[5] Hermann, R.; Krener, A.: Nonlinear controllability and observability. IEEE trans. 22, 728-740 (1977) · Zbl 0396.93015
[6] Risler, J-J.: Le théorème des zéros en géométries algébrique et analytique réelles. Bull. soc. Math. France 104, 113-127 (1976)