Minimal order time invariant representation of periodic descriptor systems

A large number of results from linear time invariant system theory can be extended to periodic systems provided an equivalent time invariant system can be found. This problem has been well investigated for periodic systems which have a standard state space representation. This paper presents a numerical procedure to achieve the same for descriptor periodic systems with possibly singular descriptor matrix, in which case the monodromy matrix is not defined. It is shown that using a stacked representation of periodic systems a minimal order generalized state space description can always be obtained under system equivalence