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Discrete-time lossless bounded real lemma for multidimensional separable denominator digital systems

Necessary and sufficient conditions for a multidimensional (N-D) discrete-time lossless bounded real (DTLBR) lemma are established for N-D separable denominator digital systems. Based on this lemma, the factorization of a class of N-D FIR lossless matrices can be performed, this leads to the solution to the open problem of finding structures to cover a class of N-D FIR lossless matrices of a given degree.