Conductance matrix realization on a two‐tree port structure

Synthesis of low‐complexity mechanical networks with constrained element values

“…Since the invention of a mechanical element named “inerter,” research interest in synthesis of passive networks has revived due to the control approach utilizing passive mechanisms . As an important branch of system theory, passive network synthesis experienced its “golden era” during the 1930s to the and after the 1970s, its research interest declined despite some new developments . This field is to investigate the physical realization of passive systems as networks containing only passive components such as resistors, inductors, and capacitors and how to reduce the realization redundancy.…”

“…It is noted that the velocities related to an inertial system, which is denoted as the mechanical ground . Using the force‐current analogy, the capacitor can be completely analogous to the inerter, and the analogy between passive electrical and mechanical networks is completed . Therefore, passive network synthesis can be completely transplanted into passive mechanical network design.…”

“…[2][3][4][5][6][7][8][9][10][11][12][13] As an important branch of system theory, passive network synthesis experienced its "golden era" during the 1930s to the [14][15][16][17][18][19][20][21][22][23] and after the 1970s, its research interest declined despite some new developments. [24][25][26][27][28][29][30] This field is to investigate the physical realization of passive systems as networks containing only passive components such as resistors, inductors, and capacitors and how to reduce the realization redundancy. Noticeably, Kalman 31,32 has made an independent call for a renewed attempt in passive network synthesis.…”

Realization of a transfer function as a passive two‐port RC ladder network with a specified gain

“…To date, minimal realizations of one‐port passive networks and transformerless realizations of multi‐port passive networks are still far from being solved. Passive network synthesis has experienced a ‘golden age’ from the 1930s to the 1970s , but its research interest had declined after the 1970s and yet has seen some developments recently.…”

Synthesis of n‐port resistive networks containing 2n terminals

“…Besides, unlike one‐port networks, the transformerless realizability problem for n ‐port networks, where n > 1, has not been fully addressed, including resistive networks with n > 3. After the 1970s, interest in passive network synthesis has declined due to the development of integrated circuits despite some relatively recent developments in this field .…”