On the preservation of the observability under sampling

When a system is regulated by a digital computer, control decisions are often restricted to be taken at fixed times 0, δ, 2δ.... For a continuous time system, the resulting situation can be modelled through the constraint that the inputs applied are constant on intervals [0, δ), [δ, 2δ),.... Moreover if the system is given with a measurement map, the state is (partially) measured only at the fixed times 0, δ, 2δ,.... This paper investigates the problem of the preservation of the observability for autonomous systems ( i.e. without control)