Operator models and L-2-norm for sampled-data systems .1. Linear periodical pulse and sampled-data operators

The paper investigates the properties of a type of linear operator that defines mathematical models of a wide class of sampled-data systems under exogenous disturbances acting on sampling units and continuous-time networks. Norms of the operators under consideration in some functional spaces are calculated. Applications to various classes of sampled-data systems are considered.