Linear programming methods for discrete l1 approximation are used to provide solutions to problems of approximate identification with state space models and to problems of model validation for stable uncertain systems. Choice of model structure is studied via Kolmogorov n-width concept and a related n-width concept for state space models. Several results are given for FIR, Laguerre and Kautz models concerning their approximation properties in the space of bounded-input bounded-output (BIBO) stable systems. A robust convergence result is given for a modified least sum of absolute deviations identification algorithm for BIBO stable linear discrete-time systems. A simulation example with identification of Kautz models and subsequent model validation is given.