## Optimal Design of Switched Networks of Positive Linear Systems via Geometric Programming

- Masaki Ogura, Victor M. Preciado
- IEEE Transactions on Control of Network Systems
- 2017

- Published 2015 in ACC

In this paper we study disease spread over a randomly switched network, which is modeled by a stochastic switched differential equation based on the so called N-intertwined model for disease spread over static networks. Assuming that all the edges of the network are independently switched, we present sufficient conditions for the convergence of infection probability to zero. Though the stability theory for switched linear systems can naively derive a necessary and sufficient condition for the convergence, the condition cannot be used for large-scale networks because, for a network with n agents, it requires computing the maximum real eigenvalue of a matrix of size exponential in n. On the other hand, our conditions that are based also on the spectral theory of random matrices can be checked by computing the maximum real eigenvalue of a matrix of size exactly n.

@inproceedings{Ogura2015DiseaseSO,
title={Disease spread over randomly switched large-scale networks},
author={Masaki Ogura and Victor M. Preciado},
booktitle={ACC},
year={2015}
}