TY - JOUR
T1 - Investigating solvability and complexity of linear active networks by means of matroids
AU - Petersen, Bjørn
N1 - Copyright 1979 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
PY - 1979
Y1 - 1979
N2 - The solvability and complexity problems of finear active network are approached from a purely combinatorial point of view, using the concepts of matroid theory. Since the method is purely combinatorial, we take into account the network topology alone. Under this assumption necessary and sufficient conditions are given for the unique solvablity of linear active networks. The complexity and the number of dc-eigenfrequencies are also given. The method enables.you to decide if degeneracies are due to the topology alone, or if they are caused by special relations among network parameter values. If the network parameter values are taken into account, the complexity and number of dc-eigenfrequencies given by the method, are only upper and lower bounds, respectively. The above conditions are fairly easily checked, and the complexity and number of dc-elgenfrequencies are found, using polynomially bounded algorithms (matroid partition and intersection algorithms).
AB - The solvability and complexity problems of finear active network are approached from a purely combinatorial point of view, using the concepts of matroid theory. Since the method is purely combinatorial, we take into account the network topology alone. Under this assumption necessary and sufficient conditions are given for the unique solvablity of linear active networks. The complexity and the number of dc-eigenfrequencies are also given. The method enables.you to decide if degeneracies are due to the topology alone, or if they are caused by special relations among network parameter values. If the network parameter values are taken into account, the complexity and number of dc-eigenfrequencies given by the method, are only upper and lower bounds, respectively. The above conditions are fairly easily checked, and the complexity and number of dc-elgenfrequencies are found, using polynomially bounded algorithms (matroid partition and intersection algorithms).
U2 - 10.1109/TCS.1979.1084645
DO - 10.1109/TCS.1979.1084645
M3 - Journal article
SN - 0098-4094
VL - 26
SP - 330
EP - 342
JO - IEEE Transactions on Circuits and Systems
JF - IEEE Transactions on Circuits and Systems
IS - 5
ER -