TY - JOUR
T1 - Sufficient Condition for State-Space Representation of N-D Discrete-Time Lossless Bounded Real Matrix and N-D Stability of Mansour Matrix
AU - Matsumoto, N.
AU - Anderson, B. D.O.
AU - Mansour, M.
PY - 1990/9
Y1 - 1990/9
N2 - The definition of an N-D discrete time lossless bounded real (DTLBR) matrix and sufficient conditions on a state space representation to correspond to an Af-D DTLBR matrix are given. Based on these sufficient conditions, it is shown that the transfer function of the n-D lattice filter, which is obtained from a stable 1-D lattice filter by replacing each delay element z with zi (i = 1,2,⋯, n), becomes an n-D DTLBR function. From this fact an n × n Mansour matrix, which is an A -matrix of the state space representation of a 1-D lattice filter, is proved to be stable for any dimension up to n, if it is stable in the one-dimensional case.
AB - The definition of an N-D discrete time lossless bounded real (DTLBR) matrix and sufficient conditions on a state space representation to correspond to an Af-D DTLBR matrix are given. Based on these sufficient conditions, it is shown that the transfer function of the n-D lattice filter, which is obtained from a stable 1-D lattice filter by replacing each delay element z with zi (i = 1,2,⋯, n), becomes an n-D DTLBR function. From this fact an n × n Mansour matrix, which is an A -matrix of the state space representation of a 1-D lattice filter, is proved to be stable for any dimension up to n, if it is stable in the one-dimensional case.
UR - http://www.scopus.com/inward/record.url?scp=0025483482&partnerID=8YFLogxK
U2 - 10.1109/31.57603
DO - 10.1109/31.57603
M3 - Article
AN - SCOPUS:0025483482
SN - 0098-4094
VL - 37
SP - 1151
EP - 1157
JO - IEEE Transactions on Circuits and Systems
JF - IEEE Transactions on Circuits and Systems
IS - 9
ER -