# Article

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Keywords:
ordinary differential equations; observability
Summary:
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.
References:
[1] Knobloch, H. W.: Disturbance Attenuation in Control Systems, Part II: Proofs and Applications. Contributions to Nonlinear Control Theory, F. Allgöwer, H. W. Knobloch, Shaker Verlag, Herzogenrath, 2006, to appear. MR 2176539
[2] D. Flockerzi: Dissipation Inequalities and Nonlinear $H_\infty$-Theory. Contributions to Nonlinear Control Theory, F. Allgöwer, H. W. Knobloch, Shaker Verlag, Herzogenrath, 2006, to appear.

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