  Sufficient conditions for the design of a simple class of interval observers
for linear impulsive systems subject to minimum and range dwell-time
constraints are obtained and formulated in terms of infinite-dimensional linear
programs. The proposed approach is fully constructive in the sense that
suitable observer gains can be extracted from the solution of the optimization
problems and is flexible enough to be extended to include performance
constraints and parametric uncertainties. In order to be solvable, the
infinite-dimensional linear programs are relaxed using a method based on sum of
squares which is known to be asymptotically exact in the present case. Three
examples are given for illustration: the first one pertains on the interval
observation of an impulsive system under a minimum dwell-time constraint, the
second one is about the interval observation of an aperiodic sampled-data
system and the last one is about the interval observation of a linear switched
system.
