Feedback stabilization of dynamical systems with switched delays

TL;DR

This paper studies feedback stabilization of dynamical systems with switching delays caused by wireless multi-hop networks, modeling them as switching systems and analyzing stability with new computational approaches.

Contribution

It introduces a novel modeling framework for systems with switching delays as switching systems and provides NP-hardness results and approximate stability analysis methods.

Findings

NP-hardness of stability verification for these systems

A general methodology for approximate stability analysis

Identification of new design challenges requiring advanced algorithms

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.