A behavioral approach to optimal model reduction

The problem of optimal model approximation is investigated, where the angle between system behaviours is taken as approximation criterion. This problem is analyzed for linear time-invariant dynamical systems, in a behavioral setting. In particular, no assumptions are made on input-output decompositions or stability properties of systems. The class of all optimal approximate systems of state dimension one less than the state dimension of the system to-be-approximated, is characterized. Generalizations of this result are discussed and a simulation example is given.