Kalman controllability decompositions for differential-algebraic systems

We study linear differential-algebraic equations and investigate decompositions with respect to controllability prop-erties. We show that the augmented Wong sequences can be exploited for a transformation of the system into a Kalman controllability decomposition (KCD). The KCD decouples the system into a completely controllable part, an uncontrollable part given by an ordinary differential equation and an inconsistent part, which is controllable in the behavioral sense but contains no completely controllable part. This decomposition improves a known KCD from a behavioral point of view. We conclude the paper with some features of the KCD in the case of regular systems