  We propose novel quadratic performance tests for linear discrete-time
impulsive systems based on viewing these systems as feedback interconnections
of some non-impulsive linear system with an impulsive operator. In order to
systematically analyze such interconnections, we employ the framework of
integral quadratic constraints and propose novel constraints of this kind for
capturing the behavior of the involved impulsive operator. As a major benefit,
the modularity of this framework permits seamless extensions to
interconnections affected by heterogeneous uncertainties in a straightforward
fashion. This contrasts with alternative approaches which are based on
capturing the system's impulsive behavior by means of a clock. Building upon
the developed analysis criteria, we characterize the existence of non-impulsive
estimators for such impulsive interconnections in a lossless fashion and in
terms of linear matrix inequalities. Finally, our approach is illustrated by
means of several numerical examples.
