On the elimination of latent variables in ℒ2 behaviors

This paper considers the problem to eliminate latent variables from models in the class of linear shift-invariant L2 systems. Models in this class are assumed to relate manifest and latent variables by means of rational operators. The question is addressed when the induced manifest behavior of such a model again admits a representation as the L2 kernel of a rational operator. Necessary and sufficient conditions for eliminability in this class are given and are compared with earlier obtained results for classical C∞ behaviors. We also provide an explicit state space algorithm for the construction of the induced manifest behavior, which is a result from the obtained relation between elimination of variables and disturbance decoupling problems.