Sufficient Condition for State-Space Representation of N-D Discrete-Time Lossless Bounded Real Matrix and N-D Stability of Mansour Matrix
نویسندگان
چکیده
Abstr(~ct-The definition of an N-D discrete time lossless bounded real (DTLBR) matrix and sufticient conditions on a state space representation to correspond to an N-D DTLBR matrix are given. Based on these suEcient conditions, it is shown that the transfer function of the n-D lattice filter, which is obtained fmm a stable 1-D lattice filter by replacing each delay element r *th z, (i = 1.2,. . ., ,r), becomes an n-D DTLBR hnction. From this fact an n X n Mansour matrix, which is an A-matrix of the state space representation of a 1-D lattice tiller, is proved to be stable for any dimension up to n, if it is stable in the one-dimensional ease.
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