Rank invariants of nonlinear systems

A linear algebraic framework for the analysis of rank properties of nonlinear systems is introduced. This framework gives a high-level interpretation of several existing algorithms built around the recursive computation of certain algebraic ranks associated with right-invertibility, left-invertibility, and dynamic decoupling. Furthermore, it can be used to establish links between these algorithms and the differential algebraic approach, as well as to solve some static and dynamic noninteracting control problems.