Controllability of linear passive network behaviors
Systems and Control Letters
MetadataShow full item record
Hughes, T., & Smith, M. (2017). Controllability of linear passive network behaviors. Systems and Control Letters, 101 58-66. https://doi.org/10.1016/j.sysconle.2015.09.011
Classical RLC realisation 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 stabilisable, 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 stabilisable, but is marginally stabilisable. These results allow us to formalise 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 stabilisable. This paper relies substantially on the fundamental work of our late friend and colleague Jan Willems to whom the paper is dedicated.
External DOI: https://doi.org/10.1016/j.sysconle.2015.09.011
This record's URL: https://www.repository.cam.ac.uk/handle/1810/252721