Abstract— The purpose of this paper is to give a compact summary of recent results based on the concept of a regular positive-real function. We will list an efficient set of networks which is capable of realising all biquadratics which are realisable by 5-element networks or 6-element networks of seriesparallel type. The structures are simpler than the full BottDuffin synthesis, though there ar...

Relying solely on virtual springs and dampers, the transparency of standard virtual coupling suffers from the device-proxy coordination error when a large interaction force is engaged (e.g., contact tasks) and also from the unmodifiable inertias of the haptic device and the virtual proxy. To overcome these limitations, we propose a novel virtual coupling scheme, which, utilizing passive decompo...

in this paper, construction properties of branches in the root locus of a positive feedback system whose loop transfer function is not strictly proper have been investigated. we have introduced and proved the formulations for calculating the number of branches passing through infinity, point of intersection of the asymptotes on the real axis, and angle of these asymptotes with positive directio...

An approach for computing upper error bounds for reduced-order models of linear time-varying systems is presented. It is based on a transformation technique of the Hankel singular values using positive-real, odd incremented functions. By applying such time-varying functions, the singular values to be removed can be forced to become equal and constant, so that they can be reduced in one step. Tw...

We present two linked theorems on passivity: the passive behavior theorem, parts 1 and 2. Part 1 provides necessary and sufficient conditions for a general linear system, described by a set of high order differential equations, to be passive. Part 2 extends the positive-real lemma to include uncontrollable and unobservable state-space models.