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For differential equations with r parameters, 2r+1 experiments are enough for identification
Given a set of differential equations whose description involves unknown
parameters, such as reaction constants in chemical kinetics, and supposing that
one may at any time measure the values of some of the variables and possibly
apply external inputs to help excite the system, how many experiments are
sufficient in order to obtain all the information that is potentially available
about the parameters? This paper shows that the best possible answer (assuming
exact measurements) is 2r+1 experiments, where r is the number of parameters.Comment: This is a minor revision of the previously submitted report; a couple
of typos have been fixed, and some comments and two new references have been
added. Please see http://www.math.rutgers.edu/~sontag for related wor
Observability for two dimensional systems
Sufficient conditions that a two-dimensional system with output is locally observable are presented. Known results depend on time derivatives of the output and the inverse function theorem. In some cases, no informaton is provided by these theories, and one must study observability by other methods. The observability problem is dualized to the controllability problem, and the deep results of Hermes on local controllability are applied to prove a theorem concerning local observability
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