AbstractThis article proposes novel methods for the computation of state and output bounding sets for discreteâtime uncertain systems. The systems under consideration are formed from the interconnection of a nominal linear timeâinvariant system and an uncertainty operator that is known to lie within a prespecified set. The set of allowable uncertainties is described by a pointwise integral quadratic constraint (IQC), that is, a quadratic constraint that holds for all timeâsteps. Examples of pointwise IQCs characterizing common uncertainty sets are provided. The exogenous input to the system is assumed to lie in a given polytope or ellipsoid for all timeâsteps. The proposed methods are illustrated via an example.