Reverse engineering combination therapies for evolutionary dynamics of disease: An H∞ approach

We propose a general algorithm for the systematic design of feedback strategies to stabilize the evolutionary dynamics of a generic disease model using an H∞ approach. We show that designing therapy concentrations can be cast as an H∞ state feedack synthesis problem, where the feedback gain is constrained to not only be strictly diagonal, but also that its diagonal elements satisfy an overdetermined set of linear equations. Leveraging recent results in positive systems, we develop an algorithm that always yields a stabilizing controller. 

V. Jonsson, N. Matni, and R. M. Murray
Proceedings of the 52nd IEEE Conference on Decision and Control
Pages: 2060–2065
Date: December, 2013
ICB Affiliated Authors: Richard M Murray