Path-complete $p$-dominant switching linear systems

Berger, Guillaume;Fulvio, Forni;Jungers, Raphaël
(2018) 2018 IEEE Conference on Decision and Control (CDC) — Location: Miami Beach, FL, USA (17.December.2018)

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Abstract
The notion of path-complete $p$-dominance for switching linear systems (in short, path-dominance) is introduced as a way to generalize the notion of dominant/slow modes for LTI systems. Path-dominance is characterized by the contraction property of a set of quadratic cones in the state space. We show that path-dominant systems have a low-dimensional dominant behavior, and hence allow for a simplified analysis of their dynamics. An algorithm for deciding the path-dominance of a given system is presented.
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Berger, G., Fulvio, F., & Jungers, R. (2018). Path-complete $p$-dominant switching linear systems. IEEE Conference on Decision and Control. Proceedings, 6446-6451. https://doi.org/10.1109/CDC.2018.8619703 (Original work published 2018)