MATHEMATICA BOHEMICA, Vol. 131, No. 4, pp. 411-418 (2006)

Observability of nonlinear systems

H. W. Knobloch

Hans Wilhelm Knobloch, Universität Würzburg, Mathematisches Institut, Lehrstul Math. II, Am Hubland, Würzburg, D-97094, Germany

Abstract: Observability of a general nonlinear system - given in terms of an ODE $\dot {x}=f(x)$ and an output map $y=c(x)$ - is defined as in linear system theory (i.e. if $f(x)=Ax$ and $c(x)=Cx$). In contrast to standard treatment of the subject we present a criterion for observability which is not a generalization of a known linear test. It is obtained by evaluation of "approximate first integrals". This concept is borrowed from nonlinear control theory where it appears under the label "Dissipation Inequality" and serves as a link with Hamilton-Jacobi theory.

Keywords: ordinary differential equations, observability

Classification (MSC2000): 34A34, 93B07

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