Model-matching and factorization for nonlinear systems: a structural approach

The authors consider the model-matching and left-factorization problems for affine nonlinear systems in a general formulation which does not demand the compensator or the left factor to be proper, as well as in a stronger one, in which properness is required. The approach is based on the structure algorithm, which serves to define the structural invariants, rank, and structure at infinity that characterize the existence of solutions and that, more directly, is employed in constructing such solutions. Necessary and sufficient conditions for the solvability of the problems are found in terms of equalities between ranks or structures at infinity