Optimal Design of Networks of Positive Linear Systems under Stochastic Uncertainty

TL;DR

This paper develops a method to ensure stability of networks of positive linear systems under stochastic uncertainties using linear matrix inequalities and geometric programming, with applications to viral spreading models.

Contribution

It introduces a novel approach combining LMIs and geometric programming for optimal network design under stochastic uncertainty in positive linear systems.

Findings

Stability conditions are derived using LMIs for probabilistic guarantees.

An efficient geometric programming method for optimal uncertainty distribution parameters.

Application demonstrated on viral spreading process with uncertain factors.

Abstract

In this paper, we study networks of positive linear systems subject to time-invariant and random uncertainties. We present linear matrix inequalities for checking the stability of the whole network around the origin with prescribed probability and decay rate. Based on this condition, we then give an efficient method, based on geometric programming, to find the optimal parameters of the probability distribution describing the uncertainty. We illustrate our results by analyzing the stability of a viral spreading process in the presence of random uncertainties.