A Definition of Passive Linear Networks in Terms of Time and Energy

Abstract

A definition of passive linear network is made:(a) The network is linear. (b) If currents of any wave form are fed to the terminals of the network, the total energy delivered to the network is not negative.(c) No voltages appear between any pair of terminals before a current is fed to the network.When this definition is applied to two terminal networks, i.e., impedances, a necessary and sufficient condition that a two-terminal network be linear passive is that its impedance function be a positive real function.An analysis of multiterminal networks yields as a necessary and sufficient condition from the foregoing hypotheses that a certain Hermitian quadratic form be positive definite. In the case of three-terminal networks, it reduces to 4RuRu-(R!2+ R2,)i-(X 12-X 2 ,)t;;::O, where Rij+jXij=Z'i are the terms of the matrix of impedances of the network. The relation of this formula to similar but not identical formulas of Gewertz and Llewellyn, and other consequences of the condition, are discussed.

Conservatism of passivity criteria for stability analysis of trilateral haptic systems

“…For two-port networks, two well-known methods -Llewellyn's absolute stability criterion [2] and Raisbeck's passivity criterion [1] have been developed to investigate the stability of the network when connected to arbitrary passive terminations. As shown by Haykin [12], these criteria are equivalent if and only if the two-port network is symmetric.…”

“…Also, by definition, an teleoperator is absolutely stable if the teleoperation system remains stable for all possible passive terminations. For bilateral teleoperation systems comprising one master and one slave, teleoperator passivity and absolute stability can be analyzed via Raisbeck's criterion [1] and Llewellyn's criterion [2], respectively. In this paper, we discussed their counterparts for a trilateral teleoperation system.…”

Absolute Stability of 3-DOF Bilateral Haptic Systems

“…Specifically, in Raisbeck (1954), Raisbeck's method is useful as a passivity criterion for 1-DOF bilateral teleoperation systems based on the immitance matrix of the teleoperator. Shahbazi et al (2010) performed stability analysis for a dual-user (trilateral) teleoperation system based on the passivity definition for a three-port network.…”

“…For stability analysis of 1-DOF n-lateral haptic systems, passivity is used in Raisbeck (1954) for n = 2, in Shahbazi et al (2010); Panzirsch et al (2012) for n = 3, and in Mendez and Tavakoli (2010) for any n ≥ 2. Specifically, in Raisbeck (1954), Raisbeck's method is useful as a passivity criterion for 1-DOF bilateral teleoperation systems based on the immitance matrix of the teleoperator.…”

Impedance controller design of Internet-based teleoperation using absolute stability concept

“…In this paper, Raisbeck's passivity criterion [6] is used to check the passivity of the two-port. From Raisbeck's passivity criterion, a linear two-port network is passive if and only if a ) The h-parameters have no poles in the RHP; b ) Any poles of the h-parameters on the imaginary axis are simple, and the residues of the h-parameters at these poles satisfy the following conditions:…”