Sufficient conditions for the design of a simple class of interval observersfor linear impulsive systems subject to minimum and range dwell-timeconstraints are obtained and formulated in terms of infinite-dimensional linearprograms. The proposed approach is fully constructive in the sense thatsuitable observer gains can be extracted from the solution of the optimizationproblems and is flexible enough to be extended to include performanceconstraints and parametric uncertainties. In order to be solvable, theinfinite-dimensional linear programs are relaxed using a method based on sum ofsquares which is known to be asymptotically exact in the present case. Threeexamples are given for illustration: the first one pertains on the intervalobservation of an impulsive system under a minimum dwell-time constraint, thesecond one is about the interval observation of an aperiodic sampled-datasystem and the last one is about the interval observation of a linear switchedsystem.
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