# Polytopic uncertainty for linear systems: New and old complexity results

arXiv: https://arxiv.org/abs/1310.1930 · HTML: https://mlsanity.com/paper/1310.1930/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2013.

## Built on by (most cited first, 1 of 1)

- [Introducing Graph Learning over Polytopic Uncertain Graph](https://mlsanity.com/paper/2404.08176/) (2024)

## Abstract (arXiv)

We survey the problem of deciding the stability or stabilizability of uncertain linear systems whose region of uncertainty is a polytope. This natural setting has applications in many fields of applied science, from Control Theory to Systems Engineering to Biology. We focus on the algorithmic decidability of this property when one is given a particular polytope. This setting gives rise to several different algorithmic questions, depending on the nature of time (discrete/continuous), the property asked (stability/stabilizability), or the type of uncertainty (fixed/switching). Several of these questions have been answered in the literature in the last thirty years. We point out the ones that have remained open, and we answer all of them, except one which we raise as an open question. In all the cases, the results are negative in the sense that the questions are NP-hard. As a byproduct, we obtain complexity results for several other matrix problems in Systems and Control.