I am wondering if anybody has implemented, and is willing to share, a periodic Schur decomposition. The first paper mentioning it is
D. Kressner, An efficient and reliable implementation of the periodic qz algorithm IFAC Proceedings Volumes, vol. 34, no. 12, pp. 183–188, 2001.
There seems to be a Fortran code of this algorithm if one asks D. Kressner.