Abstract
LetG(z 1,z 2) be ap×m 2D proper rational transfer matrix, with full column rank, and ∑=(A 1,A 2,B 1,B 2,C, D) a state-space realization of its. Necessary and sufficient conditions are presented in this paper, which guarantee that (i)G(z 1,z 2) admits polynomial left inverses, (ii) such polynomial inverses are transfer matrices of some inverse system of ∑. When the above conditions are not fulfilled, the existence of stable and/or proper, possibly delayed, inverses ofG(z 1,z 2), is also discussed.
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Valcher, M.E., Fornasini, E. Polynomial inverses of 2D transfer matrices and finite memory realizations via inverse systems. Multidim Syst Sign Process 4, 269–284 (1993). https://doi.org/10.1007/BF00985892
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DOI: https://doi.org/10.1007/BF00985892