On the choice of input for observability in bilinear systems

For bilinear systems, observability is input dependent. This may cause problems when inputs are to be used for specific purposes (e.g., control/stabilization) while keeping the system observable. This paper may be considered as a first step towards a clarification of this situation. Specifically, it is shown that given any piecewise continuous input on an interval, there is a piecewise constant input u^*on the same interval, as close to the given input as required (in the L2-sense), which makes an observable bilinear system observable relative to u^ast. An algorithm to generate such a u^astis also given.