Directional Partial Realization Problem

摘要

The paper introduces and solves a new version of the minimal partial realization problem concerning a finite sequence of Markov parameters M(1),...,M(r) for the case when each M(j) is only specified on a subspace L(j) such that L(l) includes ... includes L(r). The results include a state space criterion for minimality, a procedure for constructing a minimal realization, and a formula for the minimal state space dimension in terms of the original data.