Regularization of linear time-invariant differential–algebraic systems

We derive equivalent criteria for the existence of a feedback ensuring that a given linear and time-invariant differential–algebraic control system is regular or autonomous, respectively. Algebraic and geometric criteria are stated in terms of the involved matrices and the augmented Wong sequences. For systems which are not regularizable by feedback, we show that an additional behavioral equivalence transformation and a reorganization of input and state variables leads to a regular system, the index of which is at most one. This procedure is known, however our approach allows for a detailed characterization of the resulting regular system.