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arXiv · 1207.5119

Feedback stabilization of dynamical systems with switched delays

Raphael M. Jungers·Alessandro D'Innocenzo·Maria D. Di Benedetto
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Abstract

We analyze a classification of two main families of controllers that are of interest when the feedback loop is subject to switching propagation delays due to routing via a wireless multi-hop communication network. We show that we can cast this problem as a subclass of classical switching systems, which is a non-trivial generalization of classical LTI systems with timevarying delays. We consider both cases where delay-dependent and delay independent controllers are used, and show that both can be modeled as switching systems with unconstrained switchings. We provide NP-hardness results for the stability verification problem, and propose a general methodology for approximate stability analysis with arbitrary precision. We finally give evidence that non-trivial design problems arise for which new algorithmic methods are needed.

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Raphael M. Jungers, Alessandro D'Innocenzo, Maria D. Di Benedetto. 2012-07-21. Feedback stabilization of dynamical systems with switched delays. https://arxiv.org/abs/1207.5119

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