Controllability of linear passive network behaviors

Accepted version
Repository DOI

Type
Article
Change log
Authors
Hughes, TH 
Smith, MC 
Abstract

© 2015 Elsevier B.V. Classical RLC realization procedures (e.g. Bott–Duffin) result in networks with uncontrollable driving-point behaviors. With this motivation, we use the behavioral framework of Jan Willems to provide a rigorous analysis of RLC networks and passive behaviors. We show that the driving-point behavior of a general RLC network is stabilizable, and controllable if the network contains only two types of elements. In contrast, we show that the full behavior of the RLC network need not be stabilizable, but is marginally stabilizable. These results allow us to formalize the phasor approach to RLC networks using the notion of sinusoidal trajectories, and to address an assumption of conventional phasor analysis. Finally, we show that any passive behavior with a hybrid representation is stabilizable. This paper relies substantially on the fundamental work of our late friend and colleague Jan Willems to whom the paper is dedicated.

Description
Keywords
Behaviors, Electric circuits, Mechanical networks, Passivity, Controllability, Stabilizability
Journal Title
Systems and Control Letters
Conference Name
Journal ISSN
0167-6911
1872-7956
Volume Title
101
Publisher
Elsevier BV