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We propose novel quadratic performance tests for linear discrete-timeimpulsive systems based on viewing these systems as feedback interconnectionsof some non-impulsive linear system with an impulsive operator. In order tosystematically analyze such interconnections, we employ the framework ofintegral quadratic constraints and propose novel constraints of this kind forcapturing the behavior of the involved impulsive operator. As a major benefit,the modularity of this framework permits seamless extensions tointerconnections affected by heterogeneous uncertainties in a straightforwardfashion. This contrasts with alternative approaches which are based oncapturing the system's impulsive behavior by means of a clock. Building uponthe developed analysis criteria, we characterize the existence of non-impulsiveestimators for such impulsive interconnections in a lossless fashion and interms of linear matrix inequalities. Finally, our approach is illustrated bymeans of several numerical examples.

IQC Based Analysis and Estimator Design for Discrete-Time Systems Affected by Impulsive Uncertainties