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.