What are the most obvious generalizations of Berlekamp Massey algorithm [1] to matrix sequences?
[1] Massey, J. L., "Shiftregister synthesis and BCH decoding", IEEE Trans. Information Theory IT15 (1): 122–127
What are the most obvious generalizations of Berlekamp Massey algorithm [1] to matrix sequences?



You might find this dissertation interesting. The author has collected many references of the Matrix versions of the BerlekampMassey algorithm (citing Rissansen, Dickinson, Thome and other papers) and its applications. 

