After the invention of a new mechanical element called 'inerter' in 2002, research interest in passive network synthesis has been revived and this field has again become active and essential.The unique compendium highlights the synthesis of passive electrical or mechanical networks, which is motivated by the vibration control based on a new type of mechanical elements named inerter. It introduces important fundamental concepts of passive network synthesis, and presents recent results on this topic.These new results concern mainly the economical realizations of low-degree functions as RLC networks (damper-spring-inerter networks), the synthesis of n-port resistive networks, and the synthesis of low-complexity mechanical networks. They can be directly applied to the optimization and design of various inerter-based mechanical control systems, such as suspension systems, vibration absorbers, building vibration systems, etc.This useful reference text provides important methodologies and results for researchers in the fields of circuit theory, vibration system control, passive systems, control theory, and electrical engineering.

A resurgence of interest in network synthesis in the last decade, motivated in part by the introduction of the inerter, has led to the need for a better understanding of the most economical way to realize a given passive impedance. This monograph outlines the main contributions to the field of passive network synthesis and presents new research into the enumerative approach and the classification of networks of restricted complexity. Passive Network Synthesis: An Approach to Classification serves as both an ideal introduction to the topic and a definitive treatment of the Ladenheim catalogue. In particular, the authors provide a new analysis and classification of the Ladenheim catalogue, building on recent work, to obtain an improved understanding of the structure and realization power of the class within the biquadratic positive-real functions. This book is intended for researchers in systems and control, real algebraic geometry, electrical and mechanical networks, and dynamics and vibration.

The aim of this text is to provide physical insight & thorough understanding of the complex-frequency domain & its application of circuits.

A rigorous treatment of the essential mathematical structure of network synthesis problems, written by an eminent researcher in the field.